Question

On an up hill hike Ted climbs at 3 mph. Going back down, he runs at 5 mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?

Answer 1

Answer: He hiked 10 miles.

Explanation:

3mi/hr x 1 2/3 hr = 5 miles. 5 mi/hr x 1 hr = 5 miles.

Answer 2

The main formula is:

Distance traveled = (average)Speed*Time.

i) when Ted Climbs up:

let D be the distance, T the time it takes Ted to climb, S_u=3mph is the speed as Ted climbs up.

then: D=3T


ii) when Ted goes down:

D is the distance, T-40 the time it takes Ted go down, S_d=5mph is the speed as Ted climbs up.

then: D=5(T-40)

equalizing the equations in i and ii:

(D=) 3T=5(T-40)
3T=5T-200
200=2T
T=100 (minutes)

the total length of the hike is T+T-40=100+100-40=160 (minutes)



Answer: 160 minutes