Problem 11 · 2018 Math Kangaroo
Hard
Logic & Word Problems
estimate-and-pick
The entrances of two student halls are 250 m apart on a straight street. The first hall has 100 students and the second has 150 students. Where should a bus stop be built so that the total of all the students' walking distances is as small as possible?
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Answer: D — directly in front of the second hall
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Hint 1 of 2
Putting the stop nearer one hall trades short walks for the bigger group against longer walks for the smaller group.
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Hint 2 of 2
Place it where the larger group walks zero distance.
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Approach: put the stop where the larger group walks nothing
- For any stop between the halls, moving it a metre toward the second hall saves 150 students a metre but costs only 100 students a metre.
- So the total distance keeps shrinking as the stop moves toward the second hall.
- The best place is directly in front of the second hall (the larger group).
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