document.write( "Question 725146: Two pipes together can fill a tank of water in 6 hours one of them takes 5 hours less than
\n" ); document.write( "the other to fill it working alone. Find the time each will take to fill the tank. \n" ); document.write( "

Algebra.Com's Answer #443980 by josmiceli(19441) $\"\"$ $\"About$

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Add their rates of filling
\n" ); document.write( "Let $\"+t+\"$ = time in hrs for the slowest pipe to fill tank
\n" ); document.write( " $\"+t+-+5+\"$ = time in hrs for the faster pipe to fill tank
\n" ); document.write( "given:
\n" ); document.write( "( 1 tank filled / t hrs ) + ( 1 tank filled / t - 5 hrs ) = ( 1 tank filled / 6 hrs )
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+-+5+%29+=+1+%2F+6+\"$
\n" ); document.write( "Multiply both sides by $\"+6t%2A%28+t+-+5+%29+\"$
\n" ); document.write( " $\"+6%2A%28+t+-+5+%29+%2B+6t+=+t%2A%28+t+-+5+%29+\"$
\n" ); document.write( " $\"+6t+-+30+%2B+6t+=+t%5E2+-+5t+\"$
\n" ); document.write( " $\"+t%5E2+-+17t+%2B+30+=+0+\"$
\n" ); document.write( " $\"+%28+t+-+15+%29%2A%28+t+-+2+%29+\"$ ( just by looking at it )
\n" ); document.write( "I get
\n" ); document.write( " $\"+t+=+15+\"$ hrs and
\n" ); document.write( " $\"+t+=+2+\"$ hrs
\n" ); document.write( "It can't be $\"+t+=+2+\"$ because I have to subtract 5 hrs for the slower pipe
\n" ); document.write( "and then I get a negative.
\n" ); document.write( "So, $\"+t+=+15+\"$ and
\n" ); document.write( " $\"+t+-+5+=+10+\"$
\n" ); document.write( "The slower pipe fills in 15 hrs
\n" ); document.write( "The faster pipe fills in 10 hrs
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+-+5+%29+=+1+%2F+6+\"$
\n" ); document.write( " $\"+1%2F15+%2B+1%2F%28+15+-+5+%29+=+1+%2F+6+\"$
\n" ); document.write( " $\"+1%2F15+%2B+1%2F10+=+1%2F6+\"$
\n" ); document.write( " $\"+2%2F30+%2B+3%2F30+=+5%2F30+\"$
\n" ); document.write( " $\"+5%2F30+=+5%2F30+\"$
\n" ); document.write( "OK \n" ); document.write( "

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