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?
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.
