Question

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?

Answer 1

So the other guy has the right work but at the end he messed up. The real answer is 10 miles.

Answer 2

It takes 40 minutes more going up or 40/60 = 0.67 hours more.

Let us say that:

t = the time required for him running down

t + 0.67 = time required for him running up

 

Since the distance of running up and down must be equal therefore:

(3 miles / hr) * (t + 0.67) = (5 miles / h) * t

3 t + 2.01 = 5 t

2 t = 2.01

t = 1.005 hr

 

So the total length of the hike is:

length = 2 * (5 miles / hr) * (1.005 hr)

length = 10.05 miles