document.write( "Question 514283: pipe A alone can fill a tank in 6 hours more than it takes pipe B alone to fill the tank. Together both pipes can fill the tank in 4 hrs. How long will it take each pipe alone to fill the tank? \n" ); document.write( "

Algebra.Com's Answer #343376 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!
pipe A alone can fill ONE tank in 6 hours more than it takes pipe B alone to fill ONE tank. Together both pipes can fill ONE tank in 4 hrs. How long will it take each pipe alone to fill ONE tank?
\n" ); document.write( "

\r\n" );
document.write( "Make this chart\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "               number        time        filling\r\n" );
document.write( "              of tanks     required      rate in\r\n" );
document.write( "               filled      in hours      tanks/hr\r\n" );
document.write( "pipe A alone\r\n" );
document.write( "pipe B alone\r\n" );
document.write( "both togther\r\n" );
document.write( "\r\n" );
document.write( "and since we are talking only about filling ONE tank, we put\r\n" );
document.write( "1 for the number of tanks filled in all three cases:\r\n" );
document.write( "\r\n" );
document.write( "               number        time        filling\r\n" );
document.write( "              of tanks     required      rate in\r\n" );
document.write( "               filled      in hours      tanks/hr\r\n" );
document.write( "pipe A alone      1\r\n" );
document.write( "pipe B alone      1\r\n" );
document.write( "both togther      1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are asked how long it will take each pipe alone to fill ONE tank.\r\n" );
document.write( "\r\n" );
document.write( "Let x = number of hours it will take pipe B alone to fill ONE tank.\r\n" );
document.write( "

\n" ); document.write( ">>...pipe A alone can fill ONE tank in 6 hours more than it takes
\n" ); document.write( "pipe B alone to fill ONE tank...<<
\n" ); document.write( "

\r\n" );
document.write( "So x+6 = number of hours it will take pipe A alone to fill the tank.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "               number        time        filling\r\n" );
document.write( "              of tanks     required      rate in\r\n" );
document.write( "               filled      in hours      tanks/hr\r\n" );
document.write( "pipe A alone      1          x+6\r\n" );
document.write( "pipe B alone      1           x\r\n" );
document.write( "both togther      1\r\n" );
document.write( "

\n" ); document.write( ">>...Together both pipes can fill ONE tank in 4 hrs...<<
\n" ); document.write( "

\r\n" );
document.write( "So fill in 4 for the time reequired for both together:\r\n" );
document.write( "\r\n" );
document.write( "               number        time        filling\r\n" );
document.write( "              of tanks     required      rate in\r\n" );
document.write( "               filled      in hours      tanks/hr\r\n" );
document.write( "pipe A alone      1          x+6\r\n" );
document.write( "pipe B alone      1           x\r\n" );
document.write( "both togther      1           4\r\n" );
document.write( "\r\n" );
document.write( "Now fill in the three rates in tanks/hr by dividing\r\n" );
document.write( "the number of tanks by the hours:\r\n" );
document.write( "\r\n" );
document.write( "               number        time        filling\r\n" );
document.write( "              of tanks     required      rate in\r\n" );
document.write( "               filled      in hours      tanks/hr\r\n" );
document.write( "pipe A alone      1          x+6         1/(x+6)\r\n" );
document.write( "pipe B alone      1           x            1/x\r\n" );
document.write( "both togther      1           4            1/4\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( "So the equation is\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "To solve that you clear of fractions and simplify to\r\n" );
document.write( "a quadratic equation.  Then you get two solutions and\r\n" );
document.write( "discard the negative one and get\r\n" );
document.write( "\r\n" );
document.write( "x = 6, which is how many hours it would take pipe B\r\n" );
document.write( "\r\n" );
document.write( "And we add 6 to that,\r\n" );
document.write( "\r\n" );
document.write( "x+6 = 12, which is how many hours it would take pipe A\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );