math
posted by Cerra on .
working together 2 people can mow a large lawn in 4 hours. One person can do the job alone one hour faster than the other person. How long does it take each person working alone to mow the lawn?

rate of faster person = 1/x
rate of slower person = 1/(x+1)
combined rate = 1/x + 1/(x+1) = (2x+1)/(x(x+1))
so time with combined rate = 1/[(2x+1)/(x(x+1))
= x(x+1)/(2x+1)
so x(x+1)/(2x+1) = 4
x^2 + x = 8x + 4
x^2  7x 4 = 0
x = (7 ± √ 65)/2
= 7.53 or a negatiave
So one takes 7.53 hours, the other 8.53 hours