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,
(5/3) x = 1/24
Equating the means and the extremes, we simplify this as follows:
(5/3) x = 1/24
5x / 3 = 1 / 24
3 = 120x
1/40 = x
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.
