Question

Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing that day?
4 mph
7 mph
10 mph
12 mph

Answer 1

Let w be the wind speed (mph). Against the wind her ground speed is 20 − w, with the wind it's 20 + w. Equal times give

2/(20 − w) = 3/(20 + w).

Solve: 2(20 + w) = 3(20 − w) → 40 + 2w = 60 − 3w → 5w = 20 → w = 4.

Answer: 4 mph.