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?
Accepted Solution
A:
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.