System of Equations: A bicycle travels at a rate of 25 mph. Three hours later, a motorcycle leaves the same place at a rate of 50 mph. In how many hours will the motorcycle catch the bicycle?

Question

A bicycle travels at a rate of 25 mph. Three hours later, a motorcycle leaves the same place at a rate of 50 mph. In how many hours will the motorcycle catch the bicycle?

Answer 1

25(T+3) = 50(T)

50T-25T = 75

25T = 75

T = 75/25 = 3 hours

in 3 hours the motorcycle went 3 x 50 = 150 miles

in 6 hours the bicycle went 6 x 25 = 150 miles