SOLUTION: It takes a smaller hose 4 times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together 20 minutes to fill the swimming pool. How long

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Question 1189793: It takes a smaller hose 4 times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together 20 minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
It takes a smaller hose 4 times as long to fill a small swimming pool as it does a larger hose.
It takes both hoses working together 20 minutes to fill the swimming pool.
How long will it take the smaller hose to fill the pool by itself?
~~~~~~~~~~~~~~~~~~~ 

The large hose works as productive as 4 small hoses.


Hence, the large and the small hoses, working together, are as productive as 5 small hoses.


Both hoses, working togeter, fill the pool in 20 minutes.


Hence, the single small hose can do this job in 20*5 = 100 minutes, or 1 hour and 40 minutes.    ANSWER

Solved mentally,  without using equations,  applying reasoning,  only.

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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 josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
                 FILL RATE       TIME (minutes) for 1 POOL

Large Hose        1/x             x

Small Hose        1/(4x)          4x            

Combined        1/x+1/(4x)        20


-



-------minutes for the large hose by itself.

----------minutes for the small hose by itself.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Here is another solution method using reasoning and simple arithmetic only -- like the method shown by tutor @ikleyn but with slightly different calculations.

The smaller hose takes 4 times as long as the larger to fill the pool, so when the two work together the larger hose does 4/5 of the work and the smaller hose does 1/5.

The two together fill the pool in 20 minutes; so the smaller hose does 1/5 of the work in 20 minutes. That means it takes the smaller hose 20*5=100 minutes to fill the pool by itself.

ANSWER: 100 minutes
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