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
