SOLUTION: It takes a smaller hose 4 times as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together 15 minutes to fill the pool. How long will

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes a smaller hose 4 times as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together 15 minutes to fill the pool. How long will       Log On


   



Question 1136315: It takes a smaller hose 4 times as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together
15 minutes to fill the pool. How long will it take the larger hose to fill the pool by itself?

Found 3 solutions by ikleyn, Alan3354, josmiceli:
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to the condition, the larger hose works as effectively, as 4 smaller hoses.


Therefore, we can interpret the other part of the condition, saying that 5 small hoses can fill the pool in 15 minutes.


It means, that ONE smaller hose fills the pool in 5*15 = 75 minutes.


Then, according to the condition, one large hose can do this job in  75%2F4 minutes = 183%2F4 minutes = 18 minutes and 45 seconds.


ANSWER.  One larger hose can fill the pool in 18 minutes and 45 seconds.


Solved mentally, without using equations.

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

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 Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It takes a smaller hose 4 times as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together
15 minutes to fill the pool. How long will it take the larger hose to fill the pool by itself?
=============================
The larger hose is equivalent to 4 of the smaller.
Together, --> 5 smaller hoses.
5 smaller hoses take 15 minutes.
1 smaller takes 75 minutes.
4 smaller or the 1 larger takes 75/4 minutes.
------------------------




Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling
+1%2F%284t%29+%2B+1%2Ft++=+1%2F15+ ( +t+ is in minutes )
Multiply both sides by +60t+
+15+%2B+60+=+4t+
+4t+=+75+
+t+=+18.75+ minutes
+.75%2A60+=+45+ sec
The larger hose takes 18 min 45 sec
by itself
----------------
check:
+1%2F75+%2B+1%2F18.75+=+1%2F15+
+.01333+%2B+.05333+=+.06666+
+.06666+=+.06666+
OK