document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189434>Question 1189434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Brooke’s empty tub fills in 20 mins with the drain plugged, and her full tub drains in 10 mins with the water off. How many minutes would it take the full tub to drain while the water is on? </SPAN>\n" );
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document.write( "The LCM of 20 and 10 is 20. This LCM value will be used for the capacity of the tub (though you can use any multiple of this).\r<BR>\n" );
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document.write( "Consider the tub's capacity is 20 gallons.\r<BR>\n" );
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document.write( "If it fills in 20 minutes, with the drain plugged, then the faucet's unit rate is <BR>\n" );
document.write( "(20 gallons)/(20 minutes) = 1 gallon per minute\r<BR>\n" );
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document.write( "If the full tub empties in 10 minutes, without the faucet going, then the unit rate here is:<BR>\n" );
document.write( "(20 gallons)/(10 minutes) = 2 gallons per minute\r<BR>\n" );
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document.write( "I will subtract the two unit rates since they work against one another. <BR>\n" );
document.write( "overall rate = fill rate - drain rate = (1 gal/min) - (2 gal/min) = -1 gal/min<BR>\n" );
document.write( "The negative result means we're losing water more than gaining it. <BR>\n" );
document.write( "The drain is winning the battle. This fits with the fact that the drain is able to get the job done faster compared to the faucet.\r<BR>\n" );
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document.write( "With the faucet on and the drain open, the drain will empty the tub faster than the faucet can fill it up. <BR>\n" );
document.write( "At some point, the tub will be empty.\r<BR>\n" );
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document.write( "Specifically, that would be 20 minutes into the scenario. This is because<BR>\n" );
document.write( "(-1 gal/min)*(20 min) = -20 gallons <BR>\n" );
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document.write( "<font color=red>Answer: 20 minutes</font><BR>\n" );
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