Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem28

Video Transcription

Question number 28.  A car left point S and drove along a straight road at a speed of 50 kilometers per hour. Then every other hour another car left S. Each car was one kilometer per hour faster  than the previous one.  The last car at a speed of 100 kilometers per hour left 50 hours after the first one.  What was the speed of the car which was in front of all the other cars 100 hours after the first car left S?  Okay, so there is a lot of information here. Let's try to tabulate it in some meaningful way. So I will compare the car with number according  to the speed it left at and then its distance after 100 hours.  And let me draw in here a table  so we can see what's going on in the problem. And let's look at car number 1.  Car number 1 drove at 50 kilometers per hour  for 100 hours. So that is the distance, 5,000 kilometers. Now car number 2 took off at 51 kilometers per hour  but it had to wait for an hour.  So it has a distance of 51 times 99 kilometers an hour which is bigger than 5,000 kilometers. Car number 3 drove at 52 kilometers per hour but only for 98 hours.  Well, that number is a larger distance than any of the previous three. So these are the distances here are increasing.  Now let's look at the last car because we certainly don't want to write down all 50 entries. Car number 50 started at 100 kilometers per hour but it had to wait 50 hours.  So it drove at, it drove for 50 hours and so that's 5,000 kilometers.  And the previous one to it drove at 99 kilometers per hour but for 51 hours.  So we see, we can even fill in one more here.  We see that we are obtaining the same numbers we had  for the initial couple of cars  but now these are increasing in the opposite direction. So the first couple of cars were getting farther and farther in distance after 100 hours.  The last couple of cars are doing the opposite. So in the middle here, there is a car that went the farthest and that's the car with number 75 that drove  at 75 kilometers an hour for 75 hours.  That is the largest distance. That's the maximum value here.  And so the answer is C, 75 kilometers per hour.

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