SOLUTION: Joe cleans his room in 7 hours. With his mom, it takes them 3 hours. How long does it take mom alone?

Question 142242: Joe cleans his room in 7 hours. With his mom, it takes them 3 hours. How long does it take mom alone?
Found 2 solutions by checkley77, stanbon:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
7*x/(7+x)=3
7x=3(7+x)
7x=21+3x
7x-3x=21
4x=21
x=21/4
x=5.25 hours for the mom cleaning the room alone.
Proof:
7*5.25/(7+5.25)=3
36.75/12.25=3
3=3
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Joe cleans his room in 7 hours. With his mom, it takes them 3 hours. How long does it take mom alone?
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Joe's rate = 1/7 job/hr
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Joe and Mom together's rate = 1/3 job/hr.
-----------------------
Mom's rate alone is 1/x job/hr
------------------------
EQUATION:
rate + rate = together rate
1/7 + 1/x = 1/3
Multiply thru by 21x to get:
3x + 21 = 7x
4x = 21
x = 21/4 = 5 1/4 hr (time it will take Mom alone)
=========================
Cheers,
Stan H.

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