document.write( "Question 186746: I typed the question incorrect the first time, SORRY...\r
\n" ); document.write( "\n" ); document.write( "Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long would it take Deb to do the job alone? \n" ); document.write( "

Algebra.Com's Answer #139987 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Together,it takes John and Deb 2 hr 55 min to sort recyclables.
\n" ); document.write( " Alone, John would require 2 more hrs than Deb.
\n" ); document.write( " How long would it take Deb to do the job alone?
\n" ); document.write( ":
\n" ); document.write( "It might be easier to do this in minutes:
\n" ); document.write( "Together: 2(60) + 55 = 175 min
\n" ); document.write( ":
\n" ); document.write( "Let t = time for D to do it alone
\n" ); document.write( "then
\n" ); document.write( "(t+120) = J's time alone:
\n" ); document.write( ";
\n" ); document.write( "A typical shared work equation (let the completed job = 1):
\n" ); document.write( " $\"175%2Ft\"$ + $\"175%2F%28t%2B120%29\"$ = 1
\n" ); document.write( "Multiply equation by t(t+120) to get rid of the denominators
\n" ); document.write( "175(t+120) + 175t = t(t+120)
\n" ); document.write( ":
\n" ); document.write( "175t + 21000 + 175t = t^2 + 120t
\n" ); document.write( ";
\n" ); document.write( "350t + 21000 = t^2 + 120t
\n" ); document.write( ":
\n" ); document.write( "0 = t^2 + 120t - 350t - 21000
\n" ); document.write( "a quadratic equation:
\n" ); document.write( "t^2 - 230t - 21000 = 0
\n" ); document.write( "Factor this to:
\n" ); document.write( "(t-300)(t+70) = 0
\n" ); document.write( "the positive solution:
\n" ); document.write( "t = 300 minutes or 5 hrs is D's time alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution:
\n" ); document.write( "(175/300) + (175/420) = 1 \n" ); document.write( "

\n" );