document.write( "Question 42401: A boy and a girl work together to type a thesis and it takes them 6 hours. It would take the girl 5 hours more than the boy to type the thesis alone. How long would each need to type the thesis alone? \n" ); document.write( "

Algebra.Com's Answer #27566 by fractalier(6550) $\"\"$ $\"About$

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Let the time it takes the boy alone to be x. Her time is then x + 5.
\n" ); document.write( "The setup for problems like this is
\n" ); document.write( "t/A + t/B = 1
\n" ); document.write( "where t is the time worked together and A and B are the individual times...so plugging in we get
\n" ); document.write( "6/x + 6/(x+5) = 1
\n" ); document.write( "now multiply thru by the lowest common denominator, here x(x+5)...and we get
\n" ); document.write( "x(x+5)[6/x + 6/(x+5) = 1]
\n" ); document.write( "6(x+5) + 6x = x(x+5)
\n" ); document.write( "6x + 30 + 6x = x^2 + 5x
\n" ); document.write( "now rearrange, factor and solve
\n" ); document.write( "x^2 - 7x - 30 = 0
\n" ); document.write( "(x - 10)(x + 3) = 0
\n" ); document.write( "x = 10 or x = -3
\n" ); document.write( "since it cannot be negative time,
\n" ); document.write( "x = 10 hours and
\n" ); document.write( "x+5 = 15 hours \n" ); document.write( "

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