document.write( "Question 550806: A reservoir can be filled by one pipe in 6 hrs and by another pipe in 8 hrs. It can be emptied by a third pipe in 10 hrs. Starting empty, how long will it take to fill the reservoir if all pipes are open? \n" ); document.write( "

Algebra.Com's Answer #359140 by Edwin McCravy(20060) $\"\"$ $\"About$

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A reservoir can be filled by one pipe in 6 hrs and by another pipe in 8 hrs. It can be emptied by a third pipe in 10 hrs. Starting empty, how long will it take to fill the reservoir if all pipes are open?
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document.write( "Let the time be x hrs to fill 1 reservoir, and fill in x for the time\r\n" );
document.write( "and 1 for the number of reservoirs\r\n" );
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document.write( "Make this chart:\r\n" );
document.write( "                       number of       time in        rate in\r\n" );
document.write( "                       reservoirs       hours      reservoirs/hour\r\n" );
document.write( "1st pipe alone              \r\n" );
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document.write( "2nd pipe alone\r\n" );
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document.write( "3rd pipe alone\r\n" );
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document.write( "All pipes together        1               x\r\n" );
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document.write( "Fill in the given times for 1st and 2nd pipes to fiil 1 reservoir.\r\n" );
document.write( "But fill in -1 for the 3rd pipe because to drain 1 reservoir is the\r\n" );
document.write( "same mathematically as \"filling -1 reservoirs\"\r\n" );
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document.write( "                       number of       time in        rate in\r\n" );
document.write( "                       reservoirs       hours      reservoirs/hour\r\n" );
document.write( "1st pipe alone            1               6  \r\n" );
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document.write( "2nd pipe alone            1               8\r\n" );
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document.write( "3rd pipe alone           -1              10\r\n" );
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document.write( "All pipes together        1               x\r\n" );
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document.write( "Now fill in the rates in reservoirs/hour by dividing reservoirs by\r\n" );
document.write( "hours:\r\n" );
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document.write( "                       number of       time in        rate in\r\n" );
document.write( "                       reservoirs       hours      reservoirs/hour\r\n" );
document.write( "1st pipe alone            1               6            \r\n" );
document.write( "2nd pipe alone            1               8             \r\n" );
document.write( "3rd pipe alone           -1              10            \r\n" );
document.write( "All pipes together        1               x            \r\n" );
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document.write( "The equation is gotten by adding the rates of the first three and\r\n" );
document.write( "setting that sum equal to the combined rate:\r\n" );
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document.write( "                         +  -  =   \r\n" );
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document.write( "Solve that and get  or  hours or 5.217391304 hrs.\r\n" );
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document.write( "Edwin

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