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. If the trip home takes 12 minutes longer than the trip to the market, how many minutes does it take Carmen to bike home?

For the same route, biking at three-quarters the speed takes four-thirds as long. Let the trip to the market take t minutes; then the trip home takes 4t/3 minutes. The difference is 4t/3 − t = t/3 = 12, so t = 36 and the ride home takes 4(36)/3 = 48 minutes. The correct choice is D, 48 min.

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