document.write( "Question 116058: Jose and Carl can retile a roof in 10 h. Working alone, Jose could do the job 4.5 h faster than Carl. How long would each man need to do the job by himself? \n" ); document.write( "

Algebra.Com's Answer #84464 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Jose and Carl can re-tile a roof in 10 h. Working alone, Jose could do the job 4.5 h faster than Carl. How long would each man need to do the job by himself?
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\n" ); document.write( "Let x = time required if J works by himself
\n" ); document.write( "Then
\n" ); document.write( "(x+4.5) = time required if C works by himself
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\n" ); document.write( "Let the completed job = 1
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\n" ); document.write( " $\"10%2Fx\"$ + $\"10%2F%28%28x%2B4.5%29%29\"$ = 1
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\n" ); document.write( "If we multiply the equation by x(x+4.5) we can get rid of the denominators
\n" ); document.write( "10(x+4.5) + 10x = x(x+4.5)(1)
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\n" ); document.write( "10x + 45 + 10x = x^2 + 4.5x
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\n" ); document.write( "20x + 45 = x^2 + 4.5x
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\n" ); document.write( "0 = x^2 + 4.5x - 20x - 45
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\n" ); document.write( "A quadratic equation:
\n" ); document.write( "x^2 - 15.5x - 45 = 0
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\n" ); document.write( "Use the quadratic formula to solve this. a=1; b=-15.5; c=-45
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\n" ); document.write( "the positive solution should be x = 18 hrs is time for J working alone
\n" ); document.write( "Then
\n" ); document.write( "18 + 4.5 = 22.5 hrs for C working alone
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\n" ); document.write( "Check solutions:
\n" ); document.write( " $\"10%2F18\"$ + $\"10%2F%2822.5%29\"$ = 1 \n" ); document.write( "

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