document.write( "Question 1113377: Bill takes 3 days to paint a house, Rory takes 4 days to paint a house and Lucy takes 5 days to paint a house. How long would it take to paint a house (to the nearest hour) if all three of them worked together? \n" ); document.write( "
Algebra.Com's Answer #728401 by math_helper(2461)\"\" \"About 
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This is a rate of work problem. The first thing is to find out how much each person does in a unit of time (we'll use 1 hour as that unit):\r
\n" ); document.write( "\n" ); document.write( " Bill: 3 days = 72 hours —> Bill paints (1/72) of a house per hour
\n" ); document.write( " Rory: 4 days = 96 hours —> Rory paints (1/96) of a house per hour
\n" ); document.write( " Lucy: 5 days = 120 hours —> Lucy paints (1/120) of a house per hour
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\n" ); document.write( "Now that we have the rate per unit of time, we can add them:\r
\n" ); document.write( "\n" ); document.write( " Together, their rate is (1/72) + (1/96) + (1/120) = (1/24)(47/60) = 47/1440 house per hour\r
\n" ); document.write( "\n" ); document.write( "That means it will take them 1440/47 hours, or approx. 30.638 hours
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\n" ); document.write( "Ans: Rounded to the nearest hour: \"+highlight%28++31+%29+\" hours
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\n" ); document.write( "Check (in 30.638 hours all 3 working together should paint one house):
\n" ); document.write( " Bill paints 30.638*(1/72) = 0.4255
\n" ); document.write( " Rory paints 30.638*(1/96) = 0.3191
\n" ); document.write( " Lucy paints 30.638*(1/120) = 0.2553
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\n" ); document.write( " and 0.4255+0.3191+0.2553 = 0.9999 (ok)\r
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