document.write( "Question 624895: An old pump takes 20 hours to drain a pool. A new pump takes 13 hours to
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Algebra.Com's Answer #393156 by Edwin McCravy(20081) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The other tutor is right. Some information was omitted.  However,\r\n" );
document.write( "I rewrote your original problem and made up the missing value:\r\n" );
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document.write( "An old pump takes 20 hours to drain a pool. A new pump takes 13 hours to\r\n" );
document.write( "drain the pool.  How long will it take for both of them working together to\r\n" );
document.write( "drain the pool?\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "                   Mumber of             hours        Draining rate\r\n" );
document.write( "                  Pools drained        required       in pools/hour\r\n" );
document.write( "Old pump\r\n" );
document.write( "New pump\r\n" );
document.write( "Both together \r\n" );
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document.write( "Let x = the number of hours it takes for both of them to drain the pool working\r\n" );
document.write( "together.  Fill this in, as well as 29 hours for the old pump and 13 hours\r\n" );
document.write( "for the new pump:\r\n" );
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document.write( "                   Mumber of             hours        Draining rate\r\n" );
document.write( "                  Pools drained        required       in pools/hour\r\n" );
document.write( "Old pump                                  20\r\n" );
document.write( "New pump                                  13\r\n" );
document.write( "Both together                              x  \r\n" );
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document.write( "In each of the three cases exactly 1 pool was drained, so we put 1 for the\r\n" );
document.write( "number of pools drained in each case:  \r\n" );
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document.write( "                   Mumber of             hours        Draining rate\r\n" );
document.write( "                  Pools drained        required       in pools/hour\r\n" );
document.write( "Old pump                1                 20\r\n" );
document.write( "New pump                1                 13\r\n" );
document.write( "Both together           1                  x\r\n" );
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document.write( "Next we fill in the draining rates in pools/hour by diving the number of pools\r\n" );
document.write( "drained by the hours.\r\n" );
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document.write( "                   Mumber of             hours        Draining rate\r\n" );
document.write( "                  Pools drained        required       in pools/hour\r\n" );
document.write( "Old pump                1                 20               1/20\r\n" );
document.write( "New pump                1                 13               1/13\r\n" );
document.write( "Both together           1                  x                1/x                \r\n" );
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document.write( "The equation comes from \r\n" );
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document.write( "                  +  =  \r\n" );
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document.write( "                         +  = \r\n" );
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document.write( "Get an LCD of 260x and multiply through\r\n" );
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document.write( "                        13x + 20x = 260\r\n" );
document.write( "                              33x = 260\r\n" );
document.write( "                                x = \r\n" );
document.write( "                                x = \r\n" );
document.write( "or about 7 hours 53 minutes.\r\n" );
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document.write( "Edwin

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