SOLUTION: One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take two hoses to fill the pool working together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take two hoses to fill the pool working together?       Log On


   

Question 1135966: One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take two hoses to fill the pool working together?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
30 minutes, both hoses together.

1%2F75%2B1%2F50

3%2F%2825%2A6%29%2B2%2F%2825%2A6%29

5%2F%2825%2A6%29

.
.

Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
The smaller hose fills  1%2F75  part of the pool volume per minute.


The larger hose fills  1%2F50  part of the pool volume per minute.


Working together, they fill  1%2F75 + 1%2F50 = 2%2F150+%2B+3%2F150 = 5%2F150 = 1%2F30  part of the pool volume per minute.


Therefore, the two hoses need 30 minutes to fill the pool working together.

Answered and solved.

-----------------

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


I work a lot with high school math team students who go to a lot of competitions where getting the answer quickly is important, without worrying about how to get the answer.

For them, they see this kind of problem frequently, so they know that the answer for the time it takes working together, when the times for the two workers individually are a and b, is (ab)/(a+b).

So for your example, the number of minutes to fill the pool using both hoses is

%2850%2A75%29%2F%2850%2B75%29+=+%2850%2A75%29%2F125+=+50%2A%283%2F5%29+=+30

Here is a quick explanation of the formula....

If the numbers of minutes needed by the two workers individually are a and b, then the fractions of the job they do in one minute are 1/a and 1/b.
Then the fraction they do together is the sum of those two fractions -- 1/a + 1/b = b/ab + a/ab = (a+b)/ab.
And then the number of minutes they need to do the job together is the reciprocal of that -- (ab)/(a+b).

And here is another easy way to reach the answer, using the numbers in your example....

The least common multiple of 75 and 50 is 150. Consider what the two hoses could do in 150 minutes.
The hose that can fill the pool in 75 minutes can fill 2 of the pools in 150 minutes.
The hose that can fill the pool in 50 minutes can fill 3 of the pools in 150 minutes.
So together the two hoses could fill 5 of the pools in 150 minutes.
So together the time they would need to fill the pool once is 150/5 = 30 minutes.