document.write( "Question 512923: It takes Sara 2 hours to paint a fence and Daniel 4 hours to paint the same fence. How long will it take to paint the fence if they work together? \n" ); document.write( "

Algebra.Com's Answer #342794 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
It takes Sara 2 hours to paint a fence and Daniel 4 hours to paint the same fence. How long will it take to paint the fence if they work together?
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Make the chart:\r\n" );
document.write( "\r\n" );
document.write( "                  Number of        Time         Rate\r\n" );
document.write( "                   fences        required        in\r\n" );
document.write( "                   painted       in hours    fences/hour\r\n" );
document.write( "Sara alone\r\n" );
document.write( "Daniel alone\r\n" );
document.write( "Both together\r\n" );
document.write( "\r\n" );
document.write( "Let x be the number of hours required for both painting together\r\n" );
document.write( "to paint 1 fence. Also we fill in the times required that are \r\n" );
document.write( "given in each of the other two cases to paint 1 fence.  Also\r\n" );
document.write( "we fill in 1 for the number of fences, since in each case only\r\n" );
document.write( "1 fence is painted:\r\n" );
document.write( "\r\n" );
document.write( "                  Number of        Time         Rate\r\n" );
document.write( "                   fences        required        in\r\n" );
document.write( "                   painted       in hours    fences/hour\r\n" );
document.write( "Sara alone            1             2\r\n" );
document.write( "Daniel alone          1             4\r\n" );
document.write( "Both together         1             x\r\n" );
document.write( "\r\n" );
document.write( "We finish the table by filling in the rates in fences/hour by \r\n" );
document.write( "dividing the number of fences painted by the number of hours \r\n" );
document.write( "required in each case:\r\n" );
document.write( "\r\n" );
document.write( "                  Number of        Time         Rate\r\n" );
document.write( "                   fences        required        in\r\n" );
document.write( "                   painted       in hours    fences/hour\r\n" );
document.write( "Sara alone            1             2             1/2\r\n" );
document.write( "Daniel alone          1             4             1/4  \r\n" );
document.write( "Both together         1             x             1/x\r\n" );
document.write( "  \r\n" );
document.write( "The equation comes from:\r\n" );
document.write( "\r\n" );
document.write( "                   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                            +  = \r\n" );
document.write( "\r\n" );
document.write( "Solve that by first clearing of fractions by multiplying both\r\n" );
document.write( "sides by LCD of 4x.\r\n" );
document.write( "\r\n" );
document.write( "Answer x =  or  hours or 1 hour and 20 minutes.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );