Working together, a man and woman could complete a job in 6 days. A man workingcqlone could do it in 5 days less than a woman could. In how much time would each other do the job alone?

Question

Working together, a man and woman could complete a job in 6 days. A man workingcqlone could do it in 5 days less than a woman could. In how much time would each other do the job alone?

Answer 1

woman's rate ---- 1/x

man's rate ----- 1/(x-5) , where x > 5
combined rate = 1/x + 1/(x-5) = (x-5 +x)/(x(x-5))
= (2x-5)/(x^2 - 5x)

(2x-5)/(x^2 - 5x) = 1/6
x^2 - 5x = 12x - 30
x^2 - 17x + 30 = 0
(x-15)(x-2) = 0
x = 15 or x =2 , but x > 5

x = 15
The woman can do the job in 15 days, the man could do it in 10 days