document.write( "Question 350666: A pool takes 6 hours to fill and 9 hours to drain. If the drain is left off for 6 hours while the pool is being filled, how long did filling the pool take? \n" ); document.write( "

Algebra.Com's Answer #250647 by Fombitz(32388) $\"\"$ $\"About$

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Rate*Time=Output
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\n" ); document.write( "Let $\"Z\"$ be the volume of the pool.
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\n" ); document.write( "Filling rate: $\"6%2AR%5Bf%5D=Z\"$
\n" ); document.write( "1. $\"R%5Bf%5D=Z%2F6\"$
\n" ); document.write( "Draining rate: $\"9%2AR%5Bd%5D=Z\"$
\n" ); document.write( "2. $\"R%5Bd%5D=Z%2F9\"$
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\n" ); document.write( "Filling while the drain is open for 6 hrs: $\"%28R%5Bf%5D-R%5Bd%5D%29%2A6=Z1\"$
\n" ); document.write( "Find $\"Z1\"$ .
\n" ); document.write( "Substituting from eq. 1 and eq. 2,
\n" ); document.write( " $\"%28Z%2F6-Z%2F9%29%2A6=Z1\"$
\n" ); document.write( " $\"Z1=Z%281-2%2F3%29=Z%2F3\"$
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\n" ); document.write( " $\"Z-Z%2F3=%282%2F3%29Z\"$ still needs to be added
\n" ); document.write( "Find that time, now the drain has been closed.
\n" ); document.write( " $\"R%5Bf%5D%2At=%282%2F3%29Z\"$
\n" ); document.write( " $\"%28Z%2F6%29%2At=%282%2F3%29Z\"$
\n" ); document.write( " $\"+t=4+\"$ hrs
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\n" ); document.write( "Total time: $\"T=6%2B4\"$
\n" ); document.write( " $\"highlight%28T=10+hrs%29\"$ \n" ); document.write( "

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