document.write( "Question 298661: Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work. \n" ); document.write( "
Algebra.Com's Answer #214767 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work.
\n" ); document.write( "----
\n" ); document.write( "Together DATA:
\n" ); document.write( "time = 6 hrs/job ; rate = 1/6 job/hr
\n" ); document.write( "---
\n" ); document.write( "Juanita DATA:
\n" ); document.write( "time = x hrs/job ; rate = 1/x job/hr
\n" ); document.write( "---
\n" ); document.write( "Rick = (x+9) hrs/job ; rate = 1/(x+9) job/hr
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "Equation:
\n" ); document.write( "rate + rate = together rate:
\n" ); document.write( "1/x + 1/(x+9) = 1/6
\n" ); document.write( "---
\n" ); document.write( "Multiply thru by 6x(x+9)
\n" ); document.write( "6(x+9) + 6x = x(x+9)
\n" ); document.write( "6x + 54 + 6x = x^2 + 9x
\n" ); document.write( "x^2 -3x - 54 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "x^2 -9x+6x - 54 = 0
\n" ); document.write( "x(x-9) + 6(x-9) = 0
\n" ); document.write( "(x-9)(x+6) = 0
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 9 (time for Juanita to do the job alone)
\n" ); document.write( "x+9 = 18 (time for Rick to do the job alone)
\n" ); document.write( "================================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
\n" );