Together, Fay and Rob can paint a house in 3 days. It would take Rob 3 times as long as it would take Fay to do it alone. How long would it take each of them..

Question

Together, Fay and Rob can paint a house in 3 days. It would take Rob 3 times as long as it would take Fay to do it alone. How long would it take each of them, working alone?

Answer 1

Fay and Rob can paint 1/3 of a house per day working together. F + R = 1/3

3 * Rob = Fay ; 3R = F

Substitute 3R for F in the first equation--

3R + R = 1/3

4R = 1/3

R = (1/3)/4 = 1/3 * 1/4 = 1/12 ; Rob can paint 1/12 of a house in one day; it would take Rob 12 days to paint the whole house.

3 * (1/12) = F ; 3/12 = 1/4 = Fay; Fay can paint 1/4 of a house in one day ; it would take Fay 4 days to paint the whole house.