document.write( "Question 1129779: Pipe A can fill a tank in five hours pipe B can fill it in two hours less than it takes pipe C, a drain pipe ,to empty the tank. with all three pipes open it takes three hours to fill the tank. how long would it take pipe C to empty it? \n" ); document.write( "

Algebra.Com's Answer #746396 by josmiceli(19441) $\"\"$ $\"About$

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Pipe A's rate of filling:
\n" ); document.write( "[ 1 tank filled ] / [ 5 hrs ]
\n" ); document.write( "Let $\"+t+\"$ = time in hrs for pipe C to empty tank
\n" ); document.write( "pipe C's rate of emptying:
\n" ); document.write( "[ 1 tank emptied ] / [ t hrs ]
\n" ); document.write( "pipe B's rate of filling:
\n" ); document.write( "[ 1 take filled ] / [ t - 2 hrs ]
\n" ); document.write( "---------------------------------
\n" ); document.write( "Add rates for A % B
\n" ); document.write( "Subtract rate for C
\n" ); document.write( " $\"+1%2F5+%2B+1%2F%28+t-2+%29+-+1%2Ft+=+1%2F3+\"$
\n" ); document.write( "Multiply both sides by $\"+3%2A5%2At%2A%28+t-2+%29+\"$
\n" ); document.write( " $\"+3t%2A%28+t-2+%29+%2B+3%2A5t+-+3%2A5%2A%28+t-2+%29+=+5t%2A%28+t-2+%29+\"$
\n" ); document.write( " $\"+3t%5E2+-+6t+%2B+15t+-+15t+%2B+30+=+5t%5E2+-+10t+\"$
\n" ); document.write( " $\"+3t%5E2+-+6t+%2B+30+=+5t%5E2+-+10t+\"$
\n" ); document.write( " $\"+2t%5E2+-+4t+-+30+=+0+\"$
\n" ); document.write( " $\"+t%5E2+-+2t+-+15+=+0+\"$
\n" ); document.write( " $\"+%28+t+-+5+%29%2A%28+t+%2B+3+%29+=+0+\"$
\n" ); document.write( " $\"+t+=+5+\"$ ( choose positive time )
\n" ); document.write( "Pipe C empties the tank in 5 hrs
\n" ); document.write( "--------------------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F5+%2B+1%2F%28+5-2%29+-+1%2F5+=+1%2F3+\"$
\n" ); document.write( " $\"+1%2F5+%2B+1%2F3+-+1%2F5+=+1%2F3+\"$
\n" ); document.write( " $\"+1%2F3+=+1%2F3+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );