document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205982>Question 1205982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One pump can fill a tank with oil in 4 hours. A second pump can fill the same tank in 3 hours. If both pumps are used at the same time, how long will they take to fill the tank?\r<BR>\n" );
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document.write( "I tried everything but the answer that I had wrote down from my teacher's answer is  12/7 hours </SPAN>\n" );
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document.write( "There are a few approaches we could take. I'll discuss two methods.\r<BR>\n" );
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document.write( "Method 1\r<BR>\n" );
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document.write( "Let's consider a tank that is 12 gallons. <BR>\n" );
document.write( "Feel free to pick any positive number you want since it turns out the capacity doesn't matter. <BR>\n" );
document.write( "I'm picking 12 because it is the LCM of 3 and 4.\r<BR>\n" );
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document.write( "Pump A fills the 12 gallon tank in 4 hours when working alone.<BR>\n" );
document.write( "The unit rate is 12/4 = 3 gallons per hour.<BR>\n" );
document.write( "Formula:  rate = (amount done)/time\r<BR>\n" );
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document.write( "Pump B fills the 12 gallon tank in 3 hours when working alone.<BR>\n" );
document.write( "Unit rate = 12/3 = 4 gallons per hour.\r<BR>\n" );
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document.write( "When both pumps work together, neither pump hindering the other, their combined rate is 3+4 = 7 gallons per hour.\r<BR>\n" );
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document.write( "Then we'll use this formula<BR>\n" );
document.write( "time = (amount done)/rate<BR>\n" );
document.write( "to determine that <font color=red>12/7 hours</font> is the amount of time it takes when both pumps work together.\r<BR>\n" );
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document.write( "Side notes:<ul><li>12/7 = 1.71429 (approximate)</li><li>1.71429 hrs = 102.8574 minutes (Multiply by 60 to convert from hours to minutes)</li><li>102.8574 min = 60 min + 42.8574 min = 1 hr + 42.8574 min</li></ul>\r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "Pump A does 1 job in 4 hours when working alone.<BR>\n" );
document.write( "\"1 job\" is defined in this case as \"filling the entire tank with oil\".<BR>\n" );
document.write( "It's unit rate is 1/4 of a job per hour.\r<BR>\n" );
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document.write( "Pump B has a unit rate of 1/3 of a job per hour through similar logic.\r<BR>\n" );
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document.write( "Combined rate = 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of a job per hour\r<BR>\n" );
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document.write( "x = number of hours to do 1 job if both pumps work together<BR>\n" );
document.write( "rate*time = amount done<BR>\n" );
document.write( "(7/12 of a job per hour)*(x hours) = 1 job<BR>\n" );
document.write( "(7/12)x = 1<BR>\n" );
document.write( "x = <font color=red>12/7 hours</font><BR>\n" );
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