Monday
May 20, 2013

# Homework Help: math

Posted by john on Monday, July 23, 2012 at 12:22am.

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?

• math - Reiny, Monday, July 23, 2012 at 8:11am

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

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