SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Algebra ->  Expressions -> SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?       Log On


   

Question 469791: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Since Sally can paint a house in 4 hours, in an hour she completes 1/4 of the house. And since John can paint the same house in 6 hours, in an hour he completes 1/6 of the house. Therefore, in one hour the sum of their combined efforts is:
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1%2F4+%2B+1%2F6
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of the job.
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Add these two fractions by converting them to the common denominator of 12 to get:
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3%2F12+%2B+2%2F12+=+5%2F12
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So in each hour they complete five twelfths of the one job.
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The question, therefore, is how many hours (call them t for time) does it take for them to complete the entire one job (that is 12 twelfths of the job). Set up the following equation:
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%285%2F12%29%2At+=+12%2F12
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Solve this equation by first multiplying both sides of the equation by 12 to eliminate the denominator of 12 and get:
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5t+=+12%29
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Solve this equation by dividing both sides by 5:
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t+=+12%2F5
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and divide 12 by 5 to get the answer:
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t+=+2.4
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So it takes 2.4 hours for them working together to paint the house. (And since there are 60 minutes in an hour, the 0.4 of an hour is 60%2A0.4+=+24 minutes.) Therefore, working together they will complete the job in 2 hours and 24 minutes.
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Hope this helps you to understand the problem better.
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