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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?

Verified Answer :

taskmasters

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.

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