All right, friends, I believe you are working on the warm-up question, and when you solve and you think you got some answers, if you can share your answer with Soham, then he can tell us how many friends says which answer should be right, then we can go from there, okay? All right. We have many friends are joining. That's good. More friends, yay. Wait, how many of our friends says A? One. Okay, one friend on my end, I believe that friend only sent me a message. That friend says A to me as well. So A got two votes so far. It's almost time guys, we only seconds to start I believe. Alright guys, welcome to another Mad Kangaroo session. Today we're going to talk about work-rate ratio and all of the above. So, the warm-up says the mass of salt and fresh water in seawater in Protaras, I believe this is one of the states or one of the places, anyway, are in the ratio 7 through 193. How many kilograms of salt are there in a thousand kilograms of seawater? I recommend you to check with what they are given. They compare the mass of salt to water. But it's fresh water guys, it's not the seawater. And this is the ratio. It says how many kilograms of salt are there in a thousand kilograms of seawater? Remember, seawater is not fresh water guys, there is a difference. Let's wait a little bit for our friends to figure out. So, do we have another answer or I will just wait a little bit more? Two more say 35. Okay. I will start. So as I told you before, you just gotta be careful what they have been given and what they are asking. The ratio is going to be between salt and fresh water. Or fresh water. But here, as you see, they say how many kilograms of salt are there in 1000 kilograms of seawater. Well, to be able to find seawater from given salt and fresh water, you should get the total, you know. They are basically, I mean, if you can get salt over total, which is salt over fresh water plus salt, which is seawater, guys. Then we can kind of set a proportion. So in that case, salt is 7 over salt plus fresh water is 7 plus 193, gives us 7 over 200, as you see. So right now, we can easily say that 200 and 1000, there is some sort of relation here. So if there is 7 kilograms of salt in total 2 kilograms of seawater, with the same logic, there is going to be X kilograms of salt in 1000 kilograms of seawater. You can either do like regular cross-multiplication, or someone calls them butterfly method, whatever. Or, you know, you can just do this like that. They call them like a butterfly method. Or guys, don't worry about the butterfly or other animals. So you can only do what? Look at here. From 200 to 1000, we both know that the relation is you just multiply by 5. Well, with same logic, when you do 7 times 5, you should get X equals 35, guys. I don't know if it does make sense. Many kiddos says 35 anyway. If there is any question, you can ask me, or ask Soham. But don't ask each other. Are we good? I believe that if there is any question, they will ask us already. All right, guys, I'm going to move on. This is the little bit summary of what we are doing. And next week, we're going to continue statistics. So far, we covered calculations, iteration numbers, number theory, algebraic thinking. Four steps of problem solving strategy. If you are joining us just right now, make sure you understand the problem. Make sure you know what they are asking. Like the remember previous question, they asked us to find the ratio. I mean, it was not part or part ratio, it was part to total ratio because seawater means salt plus fresh water. Be careful with the words, what they are saying. Plan how to solve problem. For the previous question, we said we can just have proportion. It makes sense. Then carry out your problem. Make sure you complete your calculations carefully. You cannot make by 7 over 193. It doesn't make any sense. We cannot get any relation between 193 and 1000 because it was part to whole ratio. At the end, you got to look back and check and reflect. Well, we cannot find amount of water is greater than amount of total seawater. I mean, amount of salt is greater than amount of seawater. If you get, there has to be 50 kilogram salt in 40 kilogram of seawater, that means, man, you are doing something wrong, okay? Number 4 refers that whatever you are doing, make sure it makes sense. All right. A ratio compares two or more numbers in the same unit. For example, there are 15 girls and 12 boys in the class. The ratio of girls to boys is 15 over 12. Ratios are also often simplified. We can do 15 over 12 can be written as 5 over 4. When two ratios are equivalent, they are same, 1 over 2 and 5 over 10. They are called proportional. A common real-life example is working with reciprocity. Ratios can be used to compare a part to part or a part to the whole or to whole to a part. In the example, part to part, we can compare number of girls, number of boys, or we can say part to whole, which is number of girls to the entire classroom, guys. Rate. Rate compares two quantities with different units. Remember, if we compare two different quantities with the same unit, it will be ratio, but when we have different units, it means rate. Example, we have $20 over 4 burgers, means we can pay 4 burgers $20. Or if we say 350 miles in 5 hours means that vehicle, whatever it is, takes 350 miles in 5 hours. We can even find speed, you know, with the average speed of 7 miles per hour. Anyway, or we can say 540 calories for 6 bars. We can find easily amount of calories you can get from each bar. A unit rate is a rate where the second measurement is 1. I was giving that example. 20 over 4 burgers means also 5 over 1 burger because you just divide or simplify both sides by 4, you get $5 per burger. Or in the middle one, we just divide each quantities by 5, you should get 70 miles each hour. And for the last one, if you divide each numbers by 6, you should get 90 calories each bar. If you eat that bar, you're going to get 90 calories. A common rate problem is distance equals rate times time. The rate is the comparison of distance and the time, such as 60 miles per hour. Distance problems, by using d equals rt, basically d represents distance, r is rate or speed, and t is the time. To solve the problem, be sure to use the related numbers in the same equation. For example, distance going uphill, rate of going uphill, times time it takes to go uphill. Sometimes you go uphill and downhill, they can ask different aspects of the same equation. There may be different rates in different parts of the journey. To find average rate of the whole journey, you need to have average rate is equal to total distance divided by total time. Remember, different times you may use, you may have different speeds in different time frames of your journey. That's the reason we gotta find total distance first, then divide by total time. Rate of going upstream means rate in still water minus rate of your current, whereas rate of going downstream means rate in still water plus rate of current. Similarly, for airplane flying against headwind or with tailwind. When two people or two objects are traveling in the same direction, the relative speed is the distance of their speeds. You know, think about two cars, they are going the same direction. Of course, we are looking for absolute value of the difference of their speeds. When they travel in opposite directions, they are just approaching each other quickly, then the relative speed is the sum of their speeds. For two people running in a loop in the same direction, they will meet when the faster one runs one more loop than the slower one. For two people running in a loop in opposite direction, they will meet when the sum of their distance is the length of the loop. I am gonna move on, we are almost there. Sometimes you gotta work with work problems. Some work or job problems are similar to distance problems because distance is the work done by the moving object. We can say work is equal to rate or speed times time. But unlike distance problems, work can also be done by multiple workers. If they have the same rate, then work is equal to n times r times t when n is the number of workers. As you see in that equation, when you are going to have more workers, if n increase here guys, since the work is going to be same, that means time decrease. Let's say you are planning to do some sort of work and you ask for your friends for help. Since we have more people for the same work, that means when you get more friends, that means you can do that work faster. In that equation, there is inverse relation between number of people and the time here. If the workers have different work rate, then the work is equal to combined rate times time, where the combined rate is the sum of their unit rate. For those cases, first you got to find unit rate, then you are going to multiply by time to be able to figure out what's going on. Anyway guys, let's go to the next one, which is the first question is from 2000. 25 years ago, look at that. All right. 100 pennies have the value of 100 ducats. I don't know what's that. 100 pennies have the value of 250 dollars. How many ducats have the value of 100 tellers? As you see, there is no proportion or there is no relation here between ducats and tellers. That means you need to find that to find some sort of things. Okay. Let's see how many friends are going to be able to make it. Let's start trying to do this. So far, 40 seconds passed. And we got one answer for B. Okay, one friend says answer should be B. Let's see. What about others? One say B and one say A. Great. And another one says B. All right. I believe one friend send a chat, I don't know. Guys, this is just a reminder. I might not be able to check your answer really quick. Please send a message to poll group or to send to Soham. So he should be able to check faster. One person says B. B. What was that, Soham? With another vote B. All right. And it has been two minutes, guys. I believe majority of friends got B and some friends are still working on that. Let's look. So we know that 800 pennies have the value of 100 dukats. Am I right? 800 pennies is equal to 100 dukats. So for the equation, I can switch them. I can easily say that 100 dukats, whatever it is, has the value of 800 pennies. Also, we know that they say 100 pennies has the value of 250 tellers. Guys, as you remember from the beginning of the question, I said we need to find some sort of equation or relation so we can compare dukats and the tellers. Don't worry about those numbers yet. But it's not easy to go from dukats to tellers, D to T, because the middle value is not matching. Well, we have 800 here, 100 here. I would multiply the second one by eight to be able to get the same value, you know? Let's do that. If 100 pennies has the same value as 250 tellers, in that case, 800 pennies is equal to, 250 times eight should be 2,000 tellers. In that case, guys, if you look at those two equations here, the first one here and second one here, I am just underlining, and if you focus those same values, that means we can combine them, guys. So we can say easily, oops, if you guys keep joining, that's weird. Okay, we can say easily 100 dukats has the same value as 800 pennies. Also, we know that 800 pennies has the same value as 2,000 tellers. Well, remember we said that you cannot compare penny to teller or dukat to penny, but instead, we need to compare dukat to tellers. Well, let's just cancel the middle one. If you have equation like that, like with the three different quantities, you can say that 100, actually, you know what? I'm gonna move on. Now, here, let's say 100 dukats or whatever has the same value as 2,000 tellers. Well, we have given the ratio here already, I mean, the number already. When we change the color, we can say that 100 over 2,000 is equal to, if 100 dukats has the same value as 2,000 tellers, I can say how many dukats, which is X amount of dukats, are going to have 100 tellers value. Then again, guys, if you like, you can do cross-multiplication or when you look at the relation here, from 2,000 to 100, you don't need to actually divide by 20, you know. I will do the same thing here, 100 divided by 20 gives you X equals five. Whoever says five, those friends get the right answer. Thank you so much. B is the winner for this case. Any question, guys? It's coming outside, that ridiculous noise. Anyway, no question, okay, we are good, I hope. If you have question, ask Suham, not me. Okay, oh, I just get the chance. Okay, can you explain in a different way? That is a really good question. One friend says, can you explain in a different way? Look, guys. Think about it. We have, first of all, I would, what I would do, I would just write down whatever we have given. 800 pennies is equal to 100 ducats. Also, they say 100 pennies has 250 tellers. This is what we have been given, am I right? I hope you agree with that. In that case, we have only two different equations when we compare penn to ducat or ducat to teller. But there is no comparison between ducat to teller. This is the first thing. We need to compare D and T. We gotta find some sort of relation. But there is none here. But at least, guys, if you look at here, for both of the equations, penny is the same thing. Penny is the common value. It's obvious. I believe we are good so far. So to be able to compare ducat to tellers, we have to have same value on the either right or left side. We have 800 penny and we have 100 penny. Well, if the huge numbers kind of confuse you, we can just make them smaller. I would just divide both of side by eight. For the first equation, I would get what? From this one gives us 100 penny is equal to 12.5 ducat. With the same logic, just keep the second one, 100 penny gives us 250 tellers. So far, I believe we are good. Since, I mean, when we just compare those equations by dividing, on the left side, you get one, which you can just cancel. You don't have to worry about it. On the right side, we easily compare 12.5 ducat has to have the same amount of value as 250 tellers. After we get that equation, we can say, with the same logic, how many or what's the value or how many ducat has the same value as 100 tellers. I hope until this part, until this step, we are good. I really wanna believe that. Then what we can do, guys, since we are creating proportion, we can, this is the amount of x. We can use cross multiplication. Some friends like cross multiplication as well. So, as you see, we have d and t, d and t here, we don't even have to worry about those units anyway, because we only need numerical value of x. They are gonna cancel each other. Anyway, so I will say 250 times x is equal to 100 times 12.5. In that case, we can say 250x is equal to, when you multiply them, you should get 1250. One, two, three, yep, 1250. Then we won't know that we need only one x, not 250x. Since it was multiplication, we gotta divide both sides by 250. It means, guys, x should be five. Let's say our answer is five. Any question, guys? I cannot try to make little difference. I mean, it doesn't make sense. If the numbers were kind of smaller, we could just create some sort of graph or table or chart, whatever you say, but it's not possible, man. I mean, if you have 800 or 100 as a number, I cannot just create the bar diagram with the 100 bars or 100 little tiny units. So, it's not possible. Okay, so far, one friend asked me a question. Can you explain one more time? Okay, well, I hope you get it. I have no idea if you say something. I get it, 5%, 10%, not at all, a little bit, more better. I am feeling good. Something that would work. All right, I'm gonna move on since no one says anything right now. All right, what about number two? This one, 13 years ago, and it was the question number 23. Remember, these are one of the hardest questions. The tango is a dance in pairs, each consisting of one man and one woman, obvious. At the dance evening, no more than 50 people are present. Remember, whatever they are giving, you gotta use them. No more than 50, okay? At one moment, 3 1⁄4 of the men are dancing with 4 1⁄5 of the women. Hmm, how many people are dancing at that moment? And your time starts, guys. Yeah. It has been 1 minute and 20 seconds so far. Do we have any answers yet? I guess the answer is no. One person says B and another person says D. Okay, we have B versus D. Gotcha. I really want to believe that there is not only two of our friends get something. Thank you. Bye-bye. All right, kiddos, I'm gonna start. It has been about three minutes. Do you feel you need more time so we get more answers or no? Well, we got one more for B. Okay, we have two B and one D so far, that's it? Yeah. We both know there are more than three kiddos in this classroom. Others, what's going on? If you don't get anything, at least you can just share partially what you get with us. It's about proportions, remember? That means we need to use some sort of proportion here. I'm gonna start for the sake of hopefully cover more questions, you know. Okay. First of all, whatever number we get as a total, it shouldn't be more than 50. Okay. And we know that the dance comes in pairs. One man, one woman, that's it. It's a group of two and at a certain time, let's say, they say at one moment, three-fourths of the men are dancing with four-fifths of a woman. That means at that time, we have the same number of men and women. Because for each group, we choose one man and one woman. In that case, guys, can I say three-fourths of a man is equal to four-fifths of a woman? There is no other case, man. These numbers are equal. Because you choose one man and one woman to make some sort of pair, dance pair. Okay. In that case, we have three and four because the numerators make sense, the whole number. The denominators gives us the total, which is, I mean, how many women are there and how many men are there. We don't care about this one yet. We don't care about numerators right now because they are supposed to be the same thing. Well, we have three and four. Think about what is least multiple or least common multiple, whatever, of three and four. I believe since three and four are relatively prime numbers, we can expand those fractions by multiplying each other with one of them, four, another one by three. What I meant here? I can say this one, three over four, supposed to multiply by four. And what about for women's size? Four over five, supposed to multiply by three. In that case, we get three times four is twelve. Over sixteen represents the number of men dancing over the whole amount of men, you know, every single man. And four times three is again twelve women dancing over fifteen women total. Remember, at one moment, at one moment, it can be any time, that amount of men, which is twelve out of sixteen of men, are dancing with twelve out of fifteen of the women. There is a reason I choose those numbers same. Remember, because at the beginning they say tango is danced in pairs, each consisting only one man and one woman. I hope we are good with that piece. Anyway, since we found the same numbers, the matching numbers, at one moment we can say twelve men and twelve women are dancing. What was the total? Think about that. We have sixteen total men plus fifteen women, which gives us thirty-one people at the party or whatever. Here is the deal, guys. They say at a dance evening there were no more than fifty people. Gotcha. You are saying, I know what you are thinking, you are saying, sir, how do you know the total number of people is thirty-one? You are right, it can be thirty-one or multiple of thirty-one, but thirty-one is a prime number. Even you multiply thirty-one with the smallest prime number, which is two, you should get sixty-two people. But, well, well, well, they said there were no more than fifty. Can we choose sixty-two? No, man, we cannot. We cannot choose sixty-two. That means whatever number, the simplest number we found, which is thirty-one, which is total, is correct. Then you may ask me, sir, you are saying the answer is thirty-one, but there is no thirty-one. Because I am not saying the answer is thirty-one, guys. Thirty-one gives us the number of total people here. They say, how many people are dancing? Remember, they are not saying how many people are there. Again, I am reminding you one more time. Make sure you got what they are asking. Okay, how many of them were dancing? Well, since there is a pair of people dancing, we know that twelve men plus twelve women, total twenty-four people are dancing. That means whoever said B, they get, I really want to say five points, but it's meaningless, man. Okay, I got you. I am proud of whoever said B. Thank you so much. Any questions for number two? Not yet? If you have questions, ask Soham. He can explain, so you know. Okay, no questions. Alright, guys. I assume that you got it because otherwise you would ask me. Or ask Soham. Alright, another 25 years ago question. This one was number 24 from 2000 year question. At the beginning of the game, John, Peter, and Karl had tokens in the ratio of 1 to 2 to 3. Gotcha. At the end of the game, the tokens were divided between them in the ratio of 4 to 5 to 6. What was the result of the game? You know, some of them might won, some of them might lose, some of them might get nothing. Or none of the situations listed above took place. And your time starts now. Do we get some answers, Soham? One for E. One for E? We cannot solve it? None of the informations are correct? That's sad, man. Okay. Let's see. No, someone says A. Gotcha. We have A versus E. It has been 1 minute and 45 seconds. Okay, we got another answer for A. Gotcha. We get another A. Majority of our friends says answer should be A. compared to only three answers we have more way more than three people in the classroom ways if I can get more answers I will be glad okay another person says e okay look at that a verse e there is a tie here imagine answer is neither of them that would be tough man actually answer is neither of them by the way if you're a change your answer you can't do this come on here only three answers left right now about like 34% chance I'm really set for query set a and where's the t guys look at that okay it's it has been three minutes let's see and I want to ask what about B and D gotcha you get nothing all right guys for those of course I would ask myself this question at the beginning of game the ratio of the tokens have given by those you know three friends here and at the end of the game the tokens were divided between them with another ratio I believe we all know that every single person in this classroom know that number of tokens for the same game is the same am I right I mean they don't keep adding extra tokens here we know that well if number of token is same the total let's see at the beginning of the game we have 1 over 2 or 3 or 1 2 to 3 ratio with the something multiple of 6 number of token in terms of at the beginning of the game and at the end of the game we have something multiple of 4 5 6 you know I'm adding them because I'm looking for total 15 as you see the number of tokens guys has to be multiple of both 6 and 15 well for those cases to be able to make your job really easy I would look for least common multiples okay and I wouldn't choose a thousands or whatever when you look for 6 and 15 you can just you know do skip counting this is one of the easiest method we are starting 6 6 12 18 24 30 36 whatever going and when you start 15 15 30 45 and so on if you look at those two those two sequences these are sequence you know basically we can say that 30 here and here they are the same after this piece I believe you figure out we can say that at the beginning of the game or at the end of the game the total number of tokens is 30 is the first first thing you need to think okay if there are total 30 tokens guys how can I divide those tokens between John Peter and Carl if the ratio of the tokens at the beginning of the game was 1 to 2 to 3 remember I add them all and it was multiple of 6 here well 30 divided by 6 is 5 that means first person John start with 5 and 5 times 2 is 10 second person Peter had 10 at the beginning of and Carl has 3 times 5 is 15 token these are the number of tokens they have been given at the beginning guys let's see how many of them are they going to have at the end so we can say if the number of token they have increased the resourcing whatever so you know that 4 plus 5 plus 6 is 15 and 30 divided by 15 is 2 in that case 2 is the unit here 2 times 4 is 8 John started 5 and right now John has 8 tokens interesting the another friend Peter start with 5 right now Peter has 10 nothing change oh start 10 and with 10 and as you know Carl had 15 and right now he has 6 times 2 is 12 tokens I believe you can see their starting value and ending now or we can even just start and put some sort of chart here those three we had John Peter and Carl John start with 5 and make it 8 John is one of the winner you know Peter start with 10 and nothing changed for him sad and Carl started with 15 well Carl you have no idea how to play that game and you lose three of them and right now you have 12 as you see guys if you check the choices it says John won see look at see John won yes get more Carl lost yep and Peter keep the same number of tokens yeah answer was C guys I really wonder which friend says C but that friend get some points here I am proud of you buddy I am proud of every single of you but well we have only that one friend found out find out the right answer any question for respondents remember the main logic here is if you can remember for the same game number of token at the beginning and it has to be same you know the total I am talking about by the way look like no one send us any chat or no one says any question that means we can move to next one number 4 only five years ago it was number nine if John goes to school by bus and walks back I don't know why John is doing that by the way he travels for three hours okay if he goes by bus both ways he travels travels for one hour it's a lot of distance man how long does it take him if he was both ways look if you are John I don't recommend that but because the problem you cannot solve it okay let's start the timer you right away one person answers B and B answer D and one person says 1B 1D am I right 1B and 3D oh my gosh look at that you work hard let's see Okay, we are fast. Maybe we shouldn't use too much of time here. I mean, it depends, but... Okay, it has been one minute, I just wait for one more answer, then we get a solve, you know. So, do we have one more answer about it or not yet? Oh, we got one more D. Okay, look like answer is D. Let's see if you get the right answer. Alright guys, we know that if Can goes school by bus and walks back, he travels for 3 hours. It's not really giving us too much information because he used two different vehicles. But, look at the second sentence. It says, if he goes by bus both ways, he travels for 1 hour. That means guys, think about, if he goes by bus only one way, that means he is going to travel 1 over 2 hours. Which is 0.5 hours. Am I right? Look, the bus has basically, you know, we assume that bus has the same speed, you know. Well, it took for bus to go both ways 1 hour. And, let's just say, A to B or, okay, home to school. It should be HS, my bad. From home to school, then school to home, just back. We have same exact distance when he goes home to school or school to home, you know. And, if he takes by bus, go and come back, that's both ways is 1 hour. That means each of them supposed to be 0.5 hours, guys. 30 minutes home to school, 30 minutes school to home. It's, you know, common sense, I hope. Then they say, how long does it take him if he walks both ways? Think about that. They say, go back to first sentence. If John goes to school by bus, which takes half an hour, then he travels, then he goes back by walking, the total was 3 hours. Well, we both know that when you ride the bus, when you go to school, you only take half an hour. And, the total was 3 hours. That means when he walks one way, it's going to get 2.5 hours to walk, you know. Who walks 2.5 hours? That's insane. Whatever. It's just sake of problem. It's interesting. Anyway. But, they say, it's not even enough. How long does it take him if he walks both ways? It's like he's some sort of crazy, you know, home to school, school to home. If each of them take 2.5 hours, guys, you do the math, 2.5 times 2, or 2.5 plus 2.5, whatever, you get 5 hours. And, R4, no, R5 friends get the right answer. Thank you so much, guys. Any questions for this one? Nope? Okay. Gotcha. I got you. I'm gonna move on. Alright, next one. Maybe we can solve one or two more. Let's see. Alright, number 5. Quarter and century ago, from 2010. A circus trainer needs 40 minutes to wash an elephant. His son needs 2 hours to do the same job. His son is really slow, man. In how much time, with the trainer and his son, they are gonna work together to wash 3 elephants? What do you think? Remember, we mentioned about that when we have been giving you instructions. Sometimes, for the work-related problems, they are gonna ask you, how long does it take for those workers if they work together? And, time starts. One person answers D. D, alright, we get one vote, what about others? One more person says D. Gotcha. So far, it has been 1 minute and 25 seconds, because we should get more than two people for this question. Come on. One more person says D. Gotcha. Okay. Since we have only four minutes left, I'm going to solve this one really quick. Then maybe we can just take one more question. I am trying to give you as many questions we can discuss together. Okay. So think about for those questions, guys, if you remember one of the hints, you need to find unit rate. What does it mean? Look. If trainer needs 40 minutes to wash an elephant, we are going to find in one hour how many elephants they can wash. You can say, sir, why are you working with one hour? The work itself, the definition of work here is washing elephants, you know, and we are looking for work divided by time, kind of giving their speed, which is the rate. Since time is in the denominator, we know that if we make the time one, that means we are working with unit rate. So remember, that's the reason I need to focus in one hour, what person or what partially job they can finish. Well, if the trainer wash one elephant in 40 minutes, in that case, in one hour, guys, the trainer do what? How many elephants? Can I say 1.5? Because if the same person washes 40 minutes whole elephant, another 20 minutes, which means one hour, he kind of wash half elephant. In one hour, that person washes 1.5 elephants. I believe we are good with that. With the same logic, guys, in one hour, his children, his son, okay, son do what? His son washed one elephant in two hours. That means that same son washes only half elephant in one hour, you know, because two divided by two is one basically. Anyway, so in that case, after one hour, if they were working together, guys, in one hour, guys, they should wash, they should manage to wash two elephants. Am I right? Elephants. Anyway, so you need to ask yourself in one hour, if in one hour they can wash two elephants, how long does it take for them to wash three elephants? In one hour, two elephants, that means x amount of hour or minute, whatever, three elephants. You will find 2x is equal to 3, x equals 1.5, then 1.5, there is no 1.5 hours, as you see, but when you convert that, it's going to be 90 minutes, guys, because one hour plus 30 minutes is 90 minutes. Any question for this one? Okay, we still have less than one minute, but I can just show you one more question at least. Let's just clear and show this one too. All right, check this one really quick, please. Okay, since it's almost time to go, if even we just get one answer, I'm going to start solving, okay, buddy, because we don't have too much of time left. I shouldn't take too much of your time anyway. This question says, Mark always bikes at the same speed and he always walks at the same speed. He can cover the round trip from his home to the school and back again in 20 minutes when he bikes and in 60 minutes when he walks. Yesterday, Mark started biking to school but stopped and left his bike at Eva's house on the way before finishing his trip to school on foot. On the way back, he walked to Eva's house, picked up the bike, and then he biked the rest of the way home. His total travel time was 52 minutes. What fraction of his trip did Mark make by bike? What fraction by bike? Okay, one person says B and like, I promise I'm going to start solving this. So for those type of questions, guys, they say what fraction of this trip mark made by bike? Let's say that's X fraction. Since the total is supposed to be one, you know, in that case, one over X should be he walk because bike is X, one, okay, let's just put the bike, represents by X walking ratio or walking fraction represents by one minus X guys, because the total has to be one, you know, otherwise you cannot make it. Okay. So when you multiply those ratios or those fractions with given minutes, you cancel that equation. What does it mean? So it says it took for him to do 20 minutes when he bikes, it's here, 20 minutes when he bikes. Okay. And he says X amount of fraction with bike, okay, we have 20 X plus when he, it took 60 minutes when he walks, okay, 60 time, one minus X, and the total time was 52 minutes, 52 minutes. It's all that are given here. Then you've got to solve this one, you know, 20 X plus 60 minus 60 X, oops, it should be 60 X equals 52. You know, we can just do some combined like terms, 20 X minus 6 X equals negative 40 X plus 60 is equal to 52. Let's just cancel 60 from both sides. Negative 40 X is equal to negative 8, then you just divide both sides by negative 40. That means guys, X should be one over five. Whoever says one over five, I am proud of your body, that's it. Any questions so far, guys? Okay, gotcha. I hope you learned something and also you enjoy. I enjoy too, and I'm going to see you next time, guys, take care, bye.

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