document.write( "Question 1154988: Hi, can you please help me solve this word problem? Suppose one painter can paint an entire fence in 10 hours, and a second painter takes 3 hours. How many hours would it take to paint 6 fences together? \n" ); document.write( "
Algebra.Com's Answer #777519 by Theo(13342)\"\" \"About 
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one painter can paint an entire fence in 10 hours.
\n" ); document.write( "another painter can paint the an entire fence in 3 hours.
\n" ); document.write( "presumably all fences are the same size.
\n" ); document.write( "how long for both to paint 6 fences.
\n" ); document.write( "rate * time = quantity of work.
\n" ); document.write( "quantity of work is 1 fence.
\n" ); document.write( "first painter formula becomes rate * 10 = 1
\n" ); document.write( "solve for rate to get rate = 1/10.
\n" ); document.write( "second painter formula becomes rate * 3 = 1
\n" ); document.write( "solve for rate to get rate = 1/3.
\n" ); document.write( "when they work together their rates are additive.
\n" ); document.write( "1/10 + 1/3 = 3/30 + 10/30 = 13/30
\n" ); document.write( "their combined rate is 13/30 of a fence per hour.
\n" ); document.write( "when they paint 6 fences together, their combined rate is used.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "13/30 * time = 6
\n" ); document.write( "solve for time to get:
\n" ); document.write( "time = 6 / (13/30) = 13.84615385 hours.
\n" ); document.write( "note that the first painter would take 60 hours to paint 6 fences and the second painter would take 18 hours to paint 6 fences, if each was working alone.\r
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