document.write( "Question 633238: Working together, two people can complete a task in 9 hours. Working alone, one person takes 4 hours longer than the other to complete the task. How long would it take for each person to complete the task? (Round your answers to one decimal place.)\r
\n" ); document.write( "\n" ); document.write( "slower person = . hr
\n" ); document.write( "faster person = hr \n" ); document.write( "

Algebra.Com's Answer #398759 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let

represent the time taken by the more efficient worker (#1), then

is the time taken by the other guy (#2).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "#1 can do the whole job in

hours, so he can do

of the job in one hour. Likewise #2 can do

of the job in one hour. Working together, they can do\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "of the job in 1 hour, but we are given that they can do the whole job together in 9 hours, so:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Apply the LCD (the product of the two denominators in the LHS) to add the two rational expressions in the left. Then cross-multiply and collect terms. Solve the resulting quadratic in

to get #1's time and calculate

to get #2's time.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it
\n" ); document.write( "

$\"The$

\n" ); document.write( " \n" ); document.write( "

\n" );