Math CentralQuandaries & Queries


Question from sam, a student:

Michael, can climb a mountain at 2.5km/hr on his mountain bike. he descends the mountain at 5.5km/hr. he completes the whole circuit in 7 hours. how long is the trail to the top of the mountain?

Hi Sam,

What you need to use here is that rate is distance divided by time, in this problem kilometers divided by hours. This equation has to be used twice, once for the uphill climb and then for the downhill portion. What is common to the two equations is that the distance is the same for both parts.

Suppose it takes Michael $t$ hours for the uphill portion. How long does the downhill portion take? Solve the two equations for $t.$


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