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

Rate is equal to distance per time. Going to the market, the equation is: R = D/T going back home, the rate is (¾)R, therefore the equation is: (¾)R = D/(T + 12) Since the distance is the same for both cases, equate the equations RT = (3/4)R (T + 12) T=(3/4)(T + 12) (1/4)T = 9 T = 36 T+12 = 48 It takes Carmen 48 minutes to bike home.