document.write( "Question 1198027: If Joe can paint a house in 6 hours and Sam can paint
\n" ); document.write( "the same house in 8 hours how long does it take
\n" ); document.write( "them to do in working together \n" ); document.write( "

Algebra.Com's Answer #831514 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "Joe works at the rate of  1/6 house per hour
\n" );
document.write( "Same works at the rate of 1/8 house per hour\r
\n" );
document.write( "\n" );
document.write( "Together (assuming they work without interfering with each other in any way), they work at the rate of  1/6 + 1/8  = 4/24 + 3/24 = 7/24 house per hour.\r
\n" );
document.write( "\n" );
document.write( "To paint one house (1 = 24/24), they take  (24/24)/(7/24) = 24/7 hours or about 3.42 hours (3hr 25min 43sec).\r
\n" );
document.write( "\n" );
document.write( "You can qualitatively sanity check this answer as follows:  notice each can paint the house individually in roughly 7 hours. For that rate you'd expect 3.5 hrs working together.  The obtained answer of 3.42hrs is close to this value, as one would (should) expect.   \n" );
document.write( "

\n" );