document.write( "Question 354179: john can cut and split a cord of firewood in 6 fewer hours than tim can. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone? \n" ); document.write( "
Algebra.Com's Answer #253144 by jrfrunner(365)\"\" \"About 
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let j=time John works to complete the job
\n" ); document.write( "let t=time Tim works to complete the job
\n" ); document.write( "--
\n" ); document.write( "give
\n" ); document.write( "j=t-6
\n" ); document.write( "each our working together they complete 1/j+1/t=1/(t-6) + 1/t of the job
\n" ); document.write( "together it takes 4 hours to complete the job
\n" ); document.write( "therefore 4*(1/(t-6)+1/t)=1
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\n" ); document.write( "multiply by GCD t*(t-6) both side
\n" ); document.write( "4*(t+t-6))=t*(t-6)
\n" ); document.write( "4*(2t-6)=t^2-6t
\n" ); document.write( "8t-24=t^2-6t
\n" ); document.write( "0=t^2-14t+24
\n" ); document.write( "0=(t-2)*(t-12)
\n" ); document.write( "--
\n" ); document.write( "t=2 or t=12
\n" ); document.write( "if t=2 then t-6=-4 not a solution since time has to be positive for both
\n" ); document.write( "t=12 then t-6=6
\n" ); document.write( "so Tim takes 12 hours and John takes t-6 or 6 hours working alone \n" ); document.write( "
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