document.write( "Question 334338: It takes Jimmy 20 minutes to do the dishes. Susie can do the same work in 15 minutes. How long would it take them to do the dishes if they work together? \n" ); document.write( "

Algebra.Com's Answer #239562 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

The other tutor's work is in error. He should have multiplied through\r\n" );
document.write( "by 60 not 30.

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\n" ); document.write( "\n" ); document.write( "It takes Jimmy 20 minutes to do the dishes. Susie can do the same work in 15 minutes. How long would it take them to do the dishes if they work together?
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document.write( "First let's do it in our head!  Then we'll do it by algebra:\r\n" );
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document.write( "The LCM of 20 minutes and 15 minutes is 60 minutes, so:\r\n" );
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document.write( "In 60 minutes Jimmy could do 3 sets of dishes and Susie could do 4 sets of\r\n" );
document.write( "dishes.  So together they could do 7 sets of dishes in 60 minutes, so it would\r\n" );
document.write( "only take them  or  minutes to do 1 set of dishes working together.\r\n" );
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document.write( "But your teacher doesn't want you to do it that way.  They want you to use\r\n" );
document.write( "algebra.  So we'll now do that.\r\n" );
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document.write( "Make this chart, putting 1 for the number of sets of dishes to be done.\r\n" );
document.write( "Put in their individual given times, putting x for their time together,\r\n" );
document.write( "which is what is to be found. Then we find the rates by dividing the\r\n" );
document.write( "number of sets by the time. \r\n" );
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document.write( "       Number of sets of dishes done|Time in minutes|Rate in sets of dishes/minute                       \r\n" );
document.write( "Jimmy               1               |      20       |         1/20\r\n" );
document.write( "Susie               1               |      15       |         1/15\r\n" );
document.write( "Together            1               |       x       |         1/x\r\n" );
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document.write( "Form the equation from the rats:\r\n" );
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document.write( "The sum of the individual rates = their combined rats:\r\n" );
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document.write( "                \r\n" );
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document.write( "Multiply through by LCD = 60x \r\n" );
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document.write( "                \r\n" );
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document.write( "                minutes.\r\n" );
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document.write( "Edwin

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