document.write( "Question 206584: Rick and Maura work together ans sew a quilt in 4 hrs. Working alone maura wiould need 6 hrs more than rick to sew the quilt. How long would it take each if they worked alone? \n" ); document.write( "
Algebra.Com's Answer #156158 by ankor@dixie-net.com(22740)\"\" \"About 
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Rick and Maura work together ans sew a quilt in 4 hrs.
\n" ); document.write( " Working alone Maura would need 6 hrs more than Rick to sew the quilt.
\n" ); document.write( " How long would it take each if they worked alone?
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\n" ); document.write( "Let t = time required by Rick alone
\n" ); document.write( "then
\n" ); document.write( "(t+6) = Maura alone
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\n" ); document.write( "Let the completed quilt = 1
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\n" ); document.write( "\"4%2F%28%28t%2B6%29%29\" + \"4%2Ft\" = 1
\n" ); document.write( "Multiply equation by t(t+6) to get rid of the denominators, results
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\n" ); document.write( "4t + 4(t+6) = t(t+6)
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\n" ); document.write( "4t + 4t + 24 = t^2 + 6t
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\n" ); document.write( "8t + 24 = t^2 + 6t
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\n" ); document.write( "Arrange as a quadratic on the right
\n" ); document.write( "0 = t^2 + 6t - 8t - 24
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\n" ); document.write( "t^2 - 2t - 24 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(t-6)(t+4) = 0
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\n" ); document.write( "positive solution
\n" ); document.write( "t = 6 hrs, is Rick's time alone
\n" ); document.write( "and
\n" ); document.write( "6 + 6 = 12 hrs Maura's time alone
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\n" ); document.write( "Check solution in original equation
\n" ); document.write( "\"4%2F12\" + \"4%2F6\" =
\n" ); document.write( "\"2%2F6\" + \"4%2F6\" = 1\r
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