
Arthur and Peter built a brick house in 24 days. If Arthur works two thirds as quickly as Peter, how long would each person alone take to build a brick house?
Answer:Arthur could build the house in 60 days, and Peter could build it in 40 days. Let x be the speed that Peter works, measured in houses per day. Arthur works at a speed of (2/3) x. So their total working speed is x + (2/3) x, which is (5/3) x. Since they can build one house in 24 days, we know they can build 1/24 houses per day, working together. In other words,
Equating the means and the extremes, we simplify this as follows:
So Peter can build 1/40 houses per day, or one house every 40 days. Arthur works at 2/3 the speed of Peter, so he can build (2/3)(1/40) = 1/60 houses per day, or one house every 60 days. 
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