document.write( "Question 904583: An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 20 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows? \n" ); document.write( "

Algebra.Com's Answer #548834 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Rate of filling:
\n" ); document.write( "( 1 tank ) / ( 10 min )
\n" ); document.write( "Rate of emptying:
\n" ); document.write( "( 1 tank ) / ( 20 min )
\n" ); document.write( "--------------------
\n" ); document.write( "Add the rates:
\n" ); document.write( "( minus sign means pipe empties )
\n" ); document.write( " $\"+1%2F10+-+1%2F20+=+1%2Ft+\"$
\n" ); document.write( "Multiply both sides by $\"+20t+\"$
\n" ); document.write( " $\"+2t+-+t+=+20+\"$
\n" ); document.write( " $\"+t+=+20+\"$
\n" ); document.write( "After 20 min, the tank overflows
\n" ); document.write( "-----------------------------
\n" ); document.write( "check:
\n" ); document.write( "Let $\"+x+\"$ = volume of tank filled
\n" ); document.write( "( 1 = tank filled )
\n" ); document.write( " $\"+1%2F10+-+1%2F20+=+x%2F20.1+\"$
\n" ); document.write( "( $\"+20.1+\"$ min have passed )
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+2%2F20+-+1%2F20+=+x%2F20.1+\"$
\n" ); document.write( " $\"+1%2F20+=+x%2F20.1+\"$
\n" ); document.write( " $\"+20.1+=+20x+\"$
\n" ); document.write( " $\"+x+=+1.005+\"$
\n" ); document.write( "( tank starts to overflow )\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );