IIT JEE 1982 Maths - MCQ Question 3

Algebra Level 2

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be traveled by all 200 students is to be as small as possible, then the school must be built at _________ \text{\_\_\_\_\_\_\_\_\_} .


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Town B Town A 45 km from town B 45 km from town A

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1 solution

Geoff Pilling
Nov 30, 2016

Choose some location between town A and town B. If we move one cm closer to town A then thats 150 150 cm less that students from town A must travel, and 50 50 more cm that students from town B must travel. So, 100 100 fewer total cm traveled by students for each cm closer to A you make it. Therefore, building it right on town A \boxed{\text{town A}} will minimize the total distance all the students need to travel.

Good solution, except: given the problem is in kilometers, do you want to introduce inches in the solution?

Jason Dyer Staff - 4 years, 6 months ago

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Good point. Updated

Geoff Pilling - 4 years, 6 months ago

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