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