John can cut the grass in 4 hours working by himself. When john cuts the grass with his younger brother michael, it takes 3 hours. How long would it take michael to cut the grass by himself?

Answer 1

John's rate = 1/4
Michael's rate = 1/x
combined rate = 1/4 + 1/x = (x+4)/(4x)

given:
1/( (x+4)/(4x) ) = 3
4x/(x+4) = 3
4x = 3x + 12
x = 12

Michael alone would take 12 hours

check:
combined rate = 1/4 + 1/12 = 1/3
time at combined rate = 1/(1/3) = 3