document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207781>Question 1207781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?\r<BR>\n" );
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document.write( "My equation is this:\r<BR>\n" );
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document.write( "(x/15) + (x/20) = 1\r<BR>\n" );
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document.write( "You say? </SPAN>\n" );
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document.write( "15*20 = 300\r<BR>\n" );
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document.write( "Consider a 300 gallon bathtub. It turns out this volume doesn't really matter. There's nothing special about the 300. You can pick any other positive number and the final answer will be the same at the end.\r<BR>\n" );
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document.write( "The 300 gallon tub fills up completely in 15 minutes if both faucets are on and the drain is closed.<BR>\n" );
document.write( "I'll assume that the tub starts off completely empty in this scenario.<BR>\n" );
document.write( "The fill rate is 300/15 = 20 gallons per minute.<BR>\n" );
document.write( "rate = amountDone/time\r<BR>\n" );
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document.write( "When both faucets are off and the drain is open, the 300 gallon tub empties in 20 minutes. <BR>\n" );
document.write( "I'll assume that the tub is completely full at the starting point of this scenario.<BR>\n" );
document.write( "drain rate = 300/20 = 15 gallons per minute\r<BR>\n" );
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document.write( "Now let's consider the scenario where both faucets are on and the drain is open at the same time. It's an unfortunate waste of water. <BR>\n" );
document.write( "In this situation, the fill rate and drain rate basically play a game of tug-of-war. <BR>\n" );
document.write( "The fill rate wins out ultimately since the fill rate is larger compared to the drain rate (20 > 15).<BR>\n" );
document.write( "The net fill rate is 20-15 = 5 gallons per minute.<BR>\n" );
document.write( "Despite the drain wanting to remove the water, the faucets win out at the end of the day. Though of course it will take a bit longer to fill the tub. \r<BR>\n" );
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document.write( "How long would it take for the tub to completely fill up in this case?<BR>\n" );
document.write( "rate*time = amountDone<BR>\n" );
document.write( "time = amountDone/rate<BR>\n" );
document.write( "time = (300 gallons)/(5 gallons per min)<BR>\n" );
document.write( "time = 60 minutes<BR>\n" );
document.write( "time = 1 hour<BR>\n" );
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