Question

Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes at three-quarters the rate she biked to the market. At any given time, t, the distance biked can be calculated using the formula d = rt, where d represents distance and r represents rate. If the trip home takes 12 minutes longer than the trip to the market, how many minutes does it take Carmen to bike home?

Answer 1

We will use the equation:
r t = 3/4 r ( t+12 )    /:r
t = 3/4 t + 9
t - 3/4 t = 9
1/4 t = 9
t = 9 * 4 = 36 minutes ( takes a trip to the market )
36 + 12 = 48 minutes
The ride home takes 48 minutes.