document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186570>Question 1186570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One hose can fill a goldfish pond in 60 minutes, another can fill the same pond in 40 minutes. <BR>\n" );
document.write( "Find how long it takes for the pond to fill, using both hoses. </SPAN>\n" );
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document.write( "The number of minutes it takes each hose, and the fraction of the job each hose does in 1 minute, are reciprocals.<br><BR>\n" );
document.write( "So given that hose A can fill the pond in 60 minutes, the fraction of the job it does in 1 minute is 1/60.  Similarly, the fraction of the job the other hose does in 1 minute is 1/40.<br><BR>\n" );
document.write( "Add the fractions of the job each hose does in 1 minute and obviously you get the fraction of the job they do together in 1 minute.<br><BR>\n" );
document.write( "Then, per the first paragraph in this response, the number of minutes it takes the two hoses together to fill the pond is the reciprocal of that sum.<br><BR>\n" );
document.write( "I'll let you do the computations.<br><BR>\n" );
document.write( "And here is a different method that many students prefer because it avoids all those fractions and reciprocals.<br><BR>\n" );
document.write( "Consider the least common multiple of the two given times, which is 120 minutes.<br><BR>\n" );
document.write( "In 120 minutes, the first hose could fill 120/60=2 of those pools; the other could fill 120/40=3 of those pools.  So together in 120 minutes the two together could fill 5 of the pools -- and that means together they could fill the one pool in 120/5=24 minutes.<br><BR>\n" );
document.write( "ANSWER: 24 minutes<br><BR>\n" );
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