Question 107977
John and Harry can paint a house in 10 days. when working alone John can paint the house in 30 days. How many days will it take Harry to paint the house. 
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Here's a method you can use on all these kind of problems
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Let the completed = 1, each will do a fraction that will add up to 1
It's obvious that John will complete 1/3 of the job in 10 days (10/30)
Therefore John has to do 2/3 of the job. What denominator of 10 = 2/3?
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Let x = Harry's time by himself
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{{{10/30}}} + {{{10/x}}} = 1
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Get rid of the denominators, multiply equation by 30x
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30x*{{{10/30}}} + 30x*{{{10/x}}} = 30x(1)
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Cancel out the denominators and you have;
10x + 30(10) = 30x
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10x - 30x = -300
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-20x = - 300
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x = -300/-20
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x = 15 days required by John by himself
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Check the solution by adding up the fractions
{{{10/30}}} + {{{10/15}}} =
{{{1/3}}} + {{{2/3}}} = 1
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Did this make sense to you? Any questions?