Question 118453
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together.
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Let t = time required when painting together
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Let the completed job = 1
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A simple equation:
{{{t/4}}} + {{{t/6}}} = 1
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Multiply equation by 12 to get rid of the denominators:
12*{{{t/4}}} + 12*{{{t/6}}} = 12(1)
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Cancel out the denominators and you have:
3t + 2t = 12
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5t = 12
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t = 12/5
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t = 2.4 hrs working together (and not fooling around)
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:
Check our solution in the original equation:
{{{2.4/4}}} + {{{2.4/6}}} = 
 .6 + .4 = 1, confirms out solution