Question 1140373: Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 40 minutes for the longer hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on it’s own?
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, Alan3354:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here are two methods for solving this kind of problem that are different from the standard algebraic method suggested by the other tutor. One is an algebraic alternative; the other uses logical reasoning.
Knowing different algebraic methods for solving a problem is a good thing; but being able to solve a problem by logical reasoning is also a valuable skill.
(1) algebraic alternative....
Consider the least common multiple of the two given times: 120 minutes.
In 120 minutes, the two hoses together could fill the pool 120/30 = 4 times; in 120 minutes the larger hose could fill the pool 120/40 = 3 times.
That means the smaller hose could fill the pool 1 time in 120 minutes; and of course that means it would take the smaller hose 120 minutes to fill the pool.
(2) using logical reasoning....
The larger hose can fill the pool alone in 40 minutes. So when the pool is filled by the two hoses together in 30 minutes, the larger hose itself fills 30/40 = 3/4 of the pool.
That means in those 30 minutes the smaller hose fills 1/4 of the pool; and that means it would take the smaller hose 30*4 = 120 minutes to fill the pool alone.
Answer by ikleyn(52781)  (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 it’s own?
~~~~~~~~~~~~~~~~~~~~
Pay attention on how I edited your post in order for the problem makes sense.
Two hoses, working together, fill  of the pool volume per minute.
The larger hose, working alone, fills  of the pool volume per minute.
Hence, the smaller hose fills  =  =  of the pool volume per minute, working alone.
It means that the smaller hose can fill the pool in 120 minutes = 2 hours, working alone. ANSWER
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.
/\/\/\/\/\/\/\\/
An addition after reading the post by @Alan.
It looks like I am the only tutor at this forum, who uses the word "momentarily" from time to time.
Therefore, although the post by Alan is not addressed to me directly and explicitly, I may think that it is addressed to me.
Therefore, I feel the need to answer.
1. It does not matter to me what some guy said in the Atlanta (?) airport and what Alan responded to or asked him.
2. I use the word "momentarily" not because I want to appear more intelligent than I am - I think that
I am intelligent enough even without doing it.
3. The word "soon" is a synonym, but is is not the closest synonym to "momentarily".
The closest synonym is "instantly", or "in an instant" - see Wikipedia, and it is exactly what I want to express.
Not "soon", but "momentarily".
When (and if) I want to say "soon", I will do it.
Although English is not my native language, I know enough English words to use them correctly
and to express any my thought adequately.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! it's = it is
==========================
Years ago, I was in ATL waiting to board a flight to Houston.
A guy at the podium said, "We'll be boarding flight ??? to Houston momentarily."
----
I asked him, "How momentary until we board?"
He didn't seem to know what I meant.
---
If he had said, "We'll be boarding soon ... " and I asked, "How soon?" there would have been no confusion.
Some people seem to think saying "momentarily" instead of soon makes them appear to be intelligent.
Sorry, it's just the opposite.
=================
I don't recall where "momentarily" was used.
I would never cast aspersions or belittle anyone's intelligence, or even mention another tutor by name.
-----
But, consider the statement, "We will leave momentarily."
Does that mean we will leave soon?
Or we will leave for a moment?
----
"Momentarily" injects ambiguity into the statement.
----
Then there's "hopefully." It means "with hope," from "hopeful," not "I hope."
---
"We'll go there later, hopefully." means we will go there with hope (for something), not that we hope we will go there.
---
"Thankfully" has been misused for such a long time that it's hopeless.
---
Americans are very careless with speech. IDK if that's peculiar to English speakers only.
---
When I correct and mark up papers many students are confused by my corrections and clarifications.
=====================
I won't deign to cavil the point further.
|
|
|
