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?

Question

Bianca Moyer

Mathematics

11 June, 03:47

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?

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Answers (1)

Know the Answer?

Eleanor Stevens · Answer 1

It can be easily assumed that most information's are already given in the question. Based on those information's, the answer can be deduced.

rt = [ (3/4) r] * (t + 12)

4rt = 3r (t + 12)

4rt = 3rt + 36r

4rt - 3rt = 36r

rt = 36r

t = 36

From the above deduction we can conclude that the time taken by Carmen to ride to the market is 36 minutes

Then

Time taken by Carmen to ride home = 36 + 12 = 48 minutes