Grades 7-8 Video Solutions 2022-2022_7-8

Video Transcription

Question 22. The villages A, B, C, and D are situated, not necessarily in that order, on a long straight road. The distance from A to C is 75 kilometers. The distance from B  to D is 45 kilometers. And the distance from B to C is 20 kilometers. Which of the following cannot be the distance from A to D? We can start off by drawing our long straight road.  The first piece of information we are given is the distance from A to C is 75 kilometers. So we will place villages A and C like so, and we know that the distance is 75 kilometers.  Next let's use the third piece of information. The distance from B to C is 20 kilometers. Now we do not know if this is to the left or to the right of village C, so we have to  count for both directions. It is 20 kilometers from C. That is unclear if it means it is 55 kilometers from A or 95 kilometers from A. Next we can erase everything to do with  C since it will not be relevant. I am going to restructure this a little bit, and now we can look at our second piece of information. The distance from B to D is 45 kilometers.  Again, we do not know if it is to the right or left of village B, and we do not know which  of these options for village B it will be, so we have to take into account all four possibilities.  45 kilometers to the right of B like so, 45 kilometers to the left of B like so, 45 kilometers to the right of the other B like so, and 45 kilometers to the left. With this we can  start figuring out our answer. The question was which of the following cannot be the distance  from A to D. So we can notice our first option is 10 kilometers, and we see that it is possible  for the distance marked by this red line from A to D would be 55 minus 45 kilometers or 10,  so we can cross that out. Next we look at the other top D and add 55 to 45 kilometers in this  line, and we see that it is possible that the distance from A to D would be 100 kilometers.  Now we can take a look at the bottom side. The distance from A to D in this circumstance would  be 95 minus 45, which gives us 50, so this is also a possibility. And finally, furthest distance  would be 95 plus 45, which is 140 kilometers. We are left with just one possibility. So which of the following cannot be the distance from A to D? The answer is C, 80 kilometers.

Video Summary

The problem involves determining which distance cannot be the distance from A to D among multiple configurations of villages A, B, C, and D on a straight road, given distance constraints between them. By considering all possible configurations of distances from B to C (20 km) and B to D (45 km), while keeping A to C fixed at 75 km, each potential distance from A to D is calculated. After evaluating all possibilities, it is found that 80 kilometers is the only distance that cannot be achieved between A and D. Therefore, 80 kilometers is the incorrect option.

Keywords

villages

distance constraints

configurations

straight road

incorrect distance