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 15 miles with the wind and in the same amount of time runs 4 miles against the wind. What is the rate of the wind?

Solution

let r = runners rate on a still day
let w = rate of the wind
let t = time
running with the wind the combined rate is
r + w
running against the wind the combined rate is
r - w
distance = rate x time
[1] 15 = (r + w) x t
[2] 4 = (r - w) x t
divide both sides of [1] by (r + w)
divide both sides of [2] by (r - w)
15 / (r + w) = t
4 / (r - w) = t
since they\'re both equal to t, set them equal to eachother
15/(r + w) = 4 / (r - w)
from the problem description, r = 5
15 / (5 + w) = 4 / (5 - w)
cross-multiply
15(5 - w) = 4(5 + w)
75 - 15w = 20 + 4w
19w = 55
w = 2.895