Question 1186570
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The number of minutes it takes each hose, and the fraction of the job each hose does in 1 minute, are reciprocals.<br>
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>
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>
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>
I'll let you do the computations.<br>
And here is a different method that many students prefer because it avoids all those fractions and reciprocals.<br>
Consider the least common multiple of the two given times, which is 120 minutes.<br>
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>
ANSWER: 24 minutes<br>