SOLUTION: Working together , it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the larger hose to fill the swimming pool by itself , how

Algebra ->  Expressions-with-variables -> SOLUTION: Working together , it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the larger hose to fill the swimming pool by itself , how      Log On


   

Question 1170684: Working together , it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the larger hose to fill the swimming pool by itself , how long will it take the smaller hose to fill the pool on its own
Do not do Rounding
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The time for the smaller hose alone would be x:

1%2F30=1%2F40%2B1%2Fx
-
120x%281%2F30%29=120x%281%2F40%2B1%2Fx%29
4x=3x%2B120
x=120
highlight%28x=120%29

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Working together , it takes two different sized hoses 30 minutes to fill a small swimming pool.
If it takes 40 minutes for the larger hose to fill the swimming pool by itself,
how long will it take the smaller hose to fill the pool on its own ?
~~~~~~~~~~~~~~~


            The answer by @josgarithmetic,  giving x= 12 minutes for the smaller hose,  is  INCORRECT  and  ABSURDIST.

            Therefore,  I came to bring the correct solution.


Solution 

The combined rate of work for the two hoses is  1%2F30  of the job per minute.


The rate of work of the larger hose is  1%2F40    of the job per minute.


Hence, the rate of work of the smaller hose is the difference

    1%2F30 - 1%2F40 = 4%2F120 - 3%2F120 = 1%2F120.


It means that the smaller hose will fill the pool in 120 minutes.    ANSWER


ANSWER.  120 minutes.

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.


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@josgarithmetic just corrected his post after seeing my solution.




Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Working together , it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the larger hose to fill the swimming pool by itself , how long will it take the smaller hose to fill the pool on its own
Do not do Rounding 
Can't these people see how RIDICULOUS their answers are. Throw this in the GARBAGE:cross%28highlight%28x=12%29%29

How can a SMALLER hose take a shorter amount of time to fill the pool than a larger hose? In other words, 

how can a larger hose take 40 minutes, while the smaller takes just 12 hours ?

AND

How can a SMALLER hose take a shorter amount of time to fill the pool than both hoses working together? In other words, 

how can 2 hoses, working together, take 30 hours, while the smaller takes just 12 hours?