Question 200721
 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?
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Here is an easy method to solve these "shared work" problems
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Let t = time required when they work together
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Let the completed job = 1
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Each will do fraction of the job, the fractions will add up to 1
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{{{t/4}}} + {{{t/6}}} = 1
Multiply by 12 to get rid of the denominators
12*{{{t/4}}} + 12*{{{t/6}}} = 12(1)
Cancel the denominators, results:
3t + 2t = 12
:
5t = 12
t = {{{12/5}}}
t = 2.4 hrs working together
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Check solution in original equation
{{{2.4/4}}} + {{{2.4/6}}} = 
.6 + .4 = 1
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Did that make sense to you?