document.write( "Question 1019703: Two workers finished a job in 7.5 days. How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker? \n" ); document.write( "

Algebra.Com's Answer #635659 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Two workers finished a job in 7.5 days.
\n" ); document.write( " How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
\n" ); document.write( ":
\n" ); document.write( "let t = time required by one worker to complete the job alone
\n" ); document.write( "then
\n" ); document.write( "(t+8) = time required by the other worker (shirker)
\n" ); document.write( ":
\n" ); document.write( "let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "A typical shared work equation
\n" ); document.write( " $\"7.5%2Ft\"$ + $\"7.5%2F%28%28t%2B8%29%29\"$ = 1
\n" ); document.write( "multiply by t(t+8), cancel the denominators, and you have
\n" ); document.write( "7.5(t+8) + 7.5t = t(t+8)
\n" ); document.write( "7.5t + 60 + 7.5t = t^2 + 8t
\n" ); document.write( "15t + 60 = t^2 + 8t
\n" ); document.write( "form a quadratic equation on the right
\n" ); document.write( "0 = t^2 + 8t - 15t - 60
\n" ); document.write( "t^2 - 7t - 60 = 0
\n" ); document.write( "Factor easily to
\n" ); document.write( "(t-12) (t+5) = 0
\n" ); document.write( "the positive solution is all we want here
\n" ); document.write( "t = 12 days, the first guy working alone
\n" ); document.write( "then
\n" ); document.write( "the shirker would struggle thru the job in 20 days. \n" ); document.write( "

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