document.write( "Question 195186: Kathrin and Tom together clean the garage in 3 hours. Seperatly, it takes Tom one hour more then Kathrin. How long does it take the to clean the garage seperatly? Approximate to the nearest tenth of an hour. \n" ); document.write( "

Algebra.Com's Answer #146532 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Kathrin and Tom together clean the garage in 3 hours.
\n" ); document.write( "Separatly, it takes Tom one hour more then Kathrin.
\n" ); document.write( " How long does it take the to clean the garage seperatly?
\n" ); document.write( " Approximate to the nearest tenth of an hour.
\n" ); document.write( ";
\n" ); document.write( "Let t = time required for K to do the job alone
\n" ); document.write( "then
\n" ); document.write( "(t+1) = time for T to do the same job alone
\n" ); document.write( ":
\n" ); document.write( "let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "Each will do a fraction of the job; the two fractions add up to 1
\n" ); document.write( ":
\n" ); document.write( " $\"3%2Ft\"$ + $\"3%2F%28%28t%2B1%29%29\"$ = 1
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by t(t+1)
\n" ); document.write( "t(t+1)* $\"3%2Ft\"$ + t(t+1)* $\"3%2F%28%28t%2B1%29%29\"$ = t(t+1)(1)
\n" ); document.write( "cancel out the denominators and you have:
\n" ); document.write( "3(t+1) + 3t = t(t+1)
\n" ); document.write( ":
\n" ); document.write( "3t + 3 + 3t = t^2 + t
\n" ); document.write( ":
\n" ); document.write( "6t + 3 = t^2 + t
\n" ); document.write( "arrange as a quadratic equation
\n" ); document.write( "0 = t^2 + t - 6t - 3
\n" ); document.write( ":
\n" ); document.write( "t^2 - 5t -3 = 0
\n" ); document.write( "Use the quadratic formula; a=1; b=-5; c=-3
\n" ); document.write( ":
\n" ); document.write( "Do math here:
\n" ); document.write( " $\"t+=+%28-%28-5%29+%2B-+sqrt%28-5%5E2+-+4+%2A+1+%2A+-3+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( "the positive solution:
\n" ); document.write( "t = 5.54 hrs, is K's time alone
\n" ); document.write( "and
\n" ); document.write( "6.54 = T's time alone\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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