On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run down, what is the total length of Ted's hike?
Question
Answer:
Let the total length of Ted's hike be L and the total time spent be T.The time spent going down is t, and the time spent going up is t+40 (if t is measured in minutes) or t + 2 hr/3 (if t is measured in hours). Note that t + t + 2/3 must equal T, the total hiking time, with all measurerments in hours.
Distance uphill: L = (3 mph)(t+2/3) = Distance downhill: (5 mph)(t)
We need only find t, the am't of time req'd for Ted to go up to down.
3t + 2 = 5t, or 2 = 2t, or t = 1 (hour)
It will take Ted 1 hour to descend the hill and 1 2/3 hour to ascend the hill.
The total length of Ted's hike was then 2 2/3 hours, or 2 hours 40 minutes.
By the way, the distance in each direction is (5 mph)(1 hr) = 5 miles.
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11 months ago
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