document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446383>Question 446383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Jill fills a pool with water in 30 min, jack fills a pool with water in 45 min and John fills a pool with water in 1 hour and 30 min. How long will it take if they work together.  </SPAN>\n" );
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document.write( "Answer:  <font color=red>15 minutes</font>\r<BR>\n" );
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document.write( "Reasoning<BR>\n" );
document.write( "1 hr + 30 min = 60 min + 30 min = 90 min\r<BR>\n" );
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document.write( "When working alone we have these time durations in minutes only<BR>\n" );
document.write( "Jill = 30 min<BR>\n" );
document.write( "Jack = 45 min<BR>\n" );
document.write( "John = 90 min<BR>\n" );
document.write( "The LCM of that set is 90. \r<BR>\n" );
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document.write( "Consider a pool with a capacity of 9000 gallons. This hypoethical value can be changed to anything else and the final answer will be the same at the end.<BR>\n" );
document.write( "I'm tacking a few zeros onto 90 to get some large capacity, so when we divide it later on we get integer results.\r<BR>\n" );
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document.write( "When working alone, Jill fills 9000 gallons in 30 min. Her rate is 9000/30 = 300 gallons per min.<BR>\n" );
document.write( "rate = amountDone/time\r<BR>\n" );
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document.write( "When working alone, Jack does the same job in 45 min. His rate is 9000/45 = 200 gallons per min.\r<BR>\n" );
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document.write( "And when working alone, John's rate is 100 gallons per minute because 9000/90 = 100\r<BR>\n" );
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document.write( "The unit rates for each person are then added up. The assumption is that each person doesn't hinder the other when working together.<BR>\n" );
document.write( "Eg: John doesn't slow down Jack<BR>\n" );
document.write( "Jill + Jack + John = 300+200+100 = 600<BR>\n" );
document.write( "They combine to a rate of 600 gallons per minute.\r<BR>\n" );
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document.write( "When working together, the pool gets filled in <font color=red>15 minutes</font> because (9000 gallons)/(600 gallons per min) = <font color=red>15</font><BR>\n" );
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