document.write( "Question 1163899: 2 pipes fill up a pool. When both are used to fill water, it takes 1.2 hours to fill up the pool. If one is intake pipe and one is drainage pipe, it takes 6 hours to fill up the pool. How long does each pipe alone need to fill up? \n" ); document.write( "

Algebra.Com's Answer #788147 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
2 pipes fill up a pool. When bot are used to fill water, it takes 1.2 hours to fill up the pool.
\n" ); document.write( "If one is intake pipe and one is drainage pipe, it takes 6 hours to fill up the pool. How long does each pipe alone need to fill up?
\n" ); document.write( "~~~~~~~~~~`\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the rate of the first pipe and y be the rate of the second pipe.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Notice that from the context, for each pipe, the rate filling is the same as the rate draining.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the first condition,  the combined rate    x + y  is   =  =   of the pool volume per hour.\r\n" );
document.write( "\r\n" );
document.write( "From the second condition, the net inflow rate  x - y  is    of the pool volume per hour.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So you have this system of 2 equations\r\n" );
document.write( "\r\n" );
document.write( "    x + y =     (1)\r\n" );
document.write( "\r\n" );
document.write( "    x - y = .   (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add the equations and get  2x = 1,  x = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, first pipe fills the pool in 2 hours, working alone.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, from equation (1)  \r\n" );
document.write( "\r\n" );
document.write( "    y =  - x =  -  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the second pipe fills the pool in 3 hours, working alone.\r\n" );
document.write( "

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

\n" );