Question

A women can hike 1 mph faster down a trail to archuletta lake than she can on the return trip uphill. It takes her 3 hr to get to the lake and 6 hr to return. What is her speed hiking down to the lake?

Answer 1

2 mph

Explanation:

Her time ratio (3 : 6) is the inverse of her speed ratio — 6:3 = 2:1. The difference in ratio units, 2 - 1 = 1, corresponds to a difference in speed of 1 mi/h. That is, each ratio unit represents 1 mph. The number of ratio units representing her speed to the lake (2) must then represent 2 mph.

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Consistency Check

If it takes her 3 h at 2 mi/h, the distance must be (3 h)×(2 mi/h) = 6 mi. Her speed uphill is 1 mph, so it takes her 6 h to go those 6 mi.