document.write( "Question 819307: It takes James 2 hours longer to do a certain job than it take Philip. They worked together for 3 hours; then Philip left and James finished the job for 1 hour. How long would it take each of them to do the job alone? \n" ); document.write( "

Algebra.Com's Answer #493028 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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It takes James 2 hours longer to do a certain job than it take Philip.
\n" ); document.write( " They worked together for 3 hours; then Philip left and James finished the job for 1 hour.
\n" ); document.write( " How long would it take each of them to do the job alone?
\n" ); document.write( "L
\n" ); document.write( "Let t = time required by Philip to do the job
\n" ); document.write( "then
\n" ); document.write( "(t+2) = time required by James
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "IN the shared work equation J works 4 hrs and P works 3 hrs
\n" ); document.write( " $\"4%2F%28%28t%2B2%29%29\"$ + $\"3%2Ft\"$ = 1
\n" ); document.write( "multiply by t(t+2), cancel the denominators and you have:
\n" ); document.write( "4t + 3(t+2) = t(t+2)
\n" ); document.write( "4t + 3t + 6 = t^2 + 2t
\n" ); document.write( "7t + 6 = t^2 + 2t
\n" ); document.write( "Combine to form a quadratic equation the right
\n" ); document.write( "0 = t^2 + 2t - 7t - 6
\n" ); document.write( "t^2 - 5t - 6 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(t-6)(t+1) = 0
\n" ); document.write( "The positive solution is all we want here
\n" ); document.write( "t = 6 hrs for Philip alone
\n" ); document.write( "then, obviously:
\n" ); document.write( "6 + 2 = 8 hrs for James alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "You can check this in the shared work equation
\n" ); document.write( " $\"4%2F8\"$ + $\"3%2F6\"$ = 1
\n" ); document.write( " \n" ); document.write( "

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