document.write( "Question 789061: It takes Ralph 13 hours to paint a fence. Lisa can do the same job in 9 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer to three decimal places. \n" ); document.write( "
Algebra.Com's Answer #478728 by ptaylor(2198)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Let x=amount of time needed for them to finish the fence working together
\n" ); document.write( "Ralph paints at the rate of 1/13 of the fence per hour
\n" ); document.write( "Lisa paints at the rate of 1/9 of the fence per hour
\n" ); document.write( "Together they paint at the rate of 1/13 +1/9=9/117 +13/117=22/117 of the fence per hour
\n" ); document.write( "In 30 min (1/2 hr) Ralph paints (1/2)(1/13)=1/26 of the fence leaving 25/26 of the fence to be painted
\n" ); document.write( "Now (22/117)*x=25/26 is the equation that we need to solve. The rate at which they work (22/117) times the time needed equals the amount of fence that remains to be painted (25/26) of 1 fence.\r
\n" ); document.write( "\n" ); document.write( "Multiply each side by (26)(117)
\n" ); document.write( "22*26*x=25*117
\n" ); document.write( "572x=2925
\n" ); document.write( "x=5.114 hrs\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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