Math CentralQuandaries & Queries


Question from Matthew, a student:

A ski lift carries a skier up a slope at a rate of 2 miles per hour. Following the same path down the mountain, the hiker has a rate of 4 miles per hour. If the round trip took 3 hours, how far is it from the top to the bottom of the mountain?


The key is to recall that rate = distance/time. Let d be the distance from the top to the bottom in miles, t1 be the time in hours to climb up the mountain and t2 be the time in hours to go down the mountain. Thus on the way up

2 = d/t1

and on the way down

4 = d/t2.

Thus d = 2 × t1 = 4 × t2.

But you also know t1 + t2 = 3 hours.

Can you solve the problem now?


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