SOLUTION: sally paints a house in 4 hours sam paints it in 6 hours how many hours will it take both to paint the house

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Question 76: sally paints a house in 4 hours sam paints it in 6 hours how many hours will it take both to paint the house
Found 3 solutions by ichudov, richwmiller, Alan3354:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
All these problems are rate of work problems. The key is to convert "sally paints a house in 4 hours" to her rate of work: how many houses per hour. Sally can do 1/4 house per hour. Sam can do 1/6 house per hour.
Together, if they are not quarreling or worse, their rate of work is the sum of their individual rates of work:
together they paint 1%2F4%2B1%2F6 houses per hour.
1%2F4%2B1%2F6+=+3%2F12%2B2%2F12+=+5%2F12 houses per hour.
So, they would take 5/12 of an hour to paint one house, of 5%2F12%2A60+=+%285%2A60%29%2F12+=+25 minutes.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x/4+x/6=1
multiply by 12 to clear fractions
3x+2x=12
5x=12
x=12/5==2 2/5=2 hrs 24 minutes

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sally paints a house in 4 hours sam paints it in 6 hours how many hours will it take both to paint the house
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Sally does 1/4 house per hour.
Same does 1/6 house per hour.
Together, they do 1/6 + 1/4 per hour, = 5/12 per hour.
--> 12/5 hours per house.
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Use the shortcut, product/sum
4*6/(4+6) = 24/10
= 12/5