Question

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?

Answer 1

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