Question

Amy can clean the house in 7 hours. When she works together with Tom, the job takes 5 hours. How long would it take Tom, working by himself, to clean the house?

Answer 1

Amy's rate = house/7
Tom's rate = house/x

combined rate = house/7 + house/x
= (xhouse + 7house)/(7x)
= house(x+7)/(7x)

then

house/[house(x+7)/(7x) = 5
1/[(x+7)/(7x)] = 5
7x/(x+7) = 5
7x = 5x+35
2x=35
x = 35/2 or 17.5 hours

check:
combined rate = 1/17.5 + 1/7 = 2/35 + 1/7 = 1/5
time = 1/(1/5) = 5

Answer 2

Can someone explain What percentage of the work did each person do?

Answer 3

Stop cheating on thinkwell !!