SOLUTION: One hose can fill a goldfish pond in 60 minutes, another can fill the same pond in 40 minutes. Find how long it takes for the pond to fill, using both hoses.

Question 1186570: One hose can fill a goldfish pond in 60 minutes, another can fill the same pond in 40 minutes.
Find how long it takes for the pond to fill, using both hoses.
Found 3 solutions by josgarithmetic, greenestamps, Alan3354:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

One hose's rate, , pond per minutes
Another hose's rate, pond per minutes

Combined, they fill together as the sum of their rates.

and question requires the reciprocal of this.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The number of minutes it takes each hose, and the fraction of the job each hose does in 1 minute, are reciprocals.

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.

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.

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.

I'll let you do the computations.

And here is a different method that many students prefer because it avoids all those fractions and reciprocals.

Consider the least common multiple of the two given times, which is 120 minutes.

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.

ANSWER: 24 minutes

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
One hose can fill a goldfish pond in 60 minutes, another can fill the same pond in 40 minutes.
Find how long it takes for the pond to fill, using both hoses.
------------------
60*40/(60+40) = 24 minutes
RELATED QUESTIONS
one hose can fill a goldfish pond in 45 minutes and two hoses can fill the same pond in... (answered by Gmoney)
One hose can fill a goldfish pond in 84 minutes, and two hoses can fill the same pond in... (answered by nerdybill)
one hose can fill a goldfish pond in 42 minutes, and two hoses can fill the same pond in... (answered by jorel1380)
one house can fill a goldfish pond in 84 minutes, and two hoses can fill the same pond in (answered by ankor@dixie-net.com)
One hose can fill a goldfish pond and 91 minutes, and two hoses confer the same pond in... (answered by josgarithmetic,ikleyn,addingup)
One hose can fill a goldfish pond in 60 minutes, and two hoses can fill the same pond in... (answered by LinnW)
One hose can fill a goldfish pond in 45 minutes, and two hoses can fill the same pond in... (answered by nyc_function)
1 hose can fill a goldfish pond in 65 mins, and 2 hoses can the same pond in 40 mins.... (answered by nerdybill)
One hose can fill a pond in 18 minutes, and two hoses can fill the same pond in 14 min.... (answered by nerdybill)