Jim can run 5 miles per hour on level ground on a still day

Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 12 miles with the wind,and in the same amount of time runs 7 miles against the wind. What is the rate of the wind?

Solution

Speed of Jim = Vj = 5 mph

A.

speed of jim with the wind = Vj + Vw = Vw + 5

distance traveled with the wind = 12 miles

time taken = distance/speed

T1 = 12/(Vw + 5)

B.

speed of jim against the wind = Vj - Vw = 5 - Vw

distance traveled against the wind = 7 miles

time taken = distance/speed

T2 = 7/(5 - Vw)

given that

T1 = T2

12/(5 + Vw) = 7/(5 - Vw)

12*(5 - Vw) = 7*(5 + Vw)

60 - 12*Vw = 35 + 7*Vw

19*Vw = 25

Vw = 25/19 miles per hr = 1.315 miles per hr