document.write( "Question 250479: Working together, Rick & Juanita can complete a job in 6 hr. It would take Rick 9 hr longer than Juanita to do the job alone. How long would it take Juanita alone? \n" ); document.write( "

Algebra.Com's Answer #182439 by dabanfield(803) $\"\"$ $\"About$

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Working together, Rick & Juanita can complete a job in 6 hr. It would take Rick 9 hr longer than Juanita to do the job alone. How long would it take Juanita alone?\r
\n" ); document.write( "\n" ); document.write( "Let T be the time it takes for the two working together to complete the job.
\n" ); document.write( "Then 1/T is the rate that Juanita can complete the job (i.e. jobs per hour).
\n" ); document.write( "Rick's rate then is 1/(T+9).\r
\n" ); document.write( "\n" ); document.write( "So for the combined rates have:\r
\n" ); document.write( "\n" ); document.write( "((1/T) + 1/(T+9)) * 6 = 1\r
\n" ); document.write( "\n" ); document.write( "Expanding we have:\r
\n" ); document.write( "\n" ); document.write( "6/T + 6/(T+9)= 1\r
\n" ); document.write( "\n" ); document.write( "Now you can solve this for T.\r
\n" ); document.write( "\n" ); document.write( "6*(T+9) + 6 * T = T^2 + 9*
\n" ); document.write( "T^2 -3*T -54 = 0
\n" ); document.write( "(T-9)*(T+6) = 0\r
\n" ); document.write( "\n" ); document.write( "T must be poisitive so \r
\n" ); document.write( "\n" ); document.write( "T = 9 \n" ); document.write( "

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