SOLUTION: When water is turned on and passes through a small hose, your pool can be filled in 8 hours. When the water is turned on at two spigots and passes through both the small and large

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Question 1096035: When water is turned on and passes through a small hose, your pool can be filled in 8 hours. When the water is turned on at two spigots and passes through both the small and large hose, the pool can be filled in 4 hours. How long would it take to fill the pool using only the large hose?
My work:
L = Large hose
1/8 + 1/L = 1/4
1/4 - 1/8 = 1/L I will multiply both sides by 8L.
2L - L = 8
L = 8
It still seems wrong.
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Your solution is correct !


2.  You can check it:  1%2F8 + 1%2F8 = 2%2F8 = 1%2F4.


3.  Congratulations !!   Your work is perfect !

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It is a 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of filling with the small hose is:
[ 1 pool filled ] / [ 8 hrs ]
The rate of filling with both hoses is:
[ 1 pool filled ] / [ 4 hrs ]
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Let +t+ = time in hrs to fill the pool
with only the large hose
Add the rates with each hose to get the
rate with both hoses together
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+1%2F8+%2B+1%2Ft+=+1%2F4+
Multiply both sides by +8t+
+t+%2B+8+=+2t+
+t+=+8+
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I think you are right that this doesn't make sense
The only way it could be true is if both hoses were
the same size.
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I think that if one of the hoses is to be larger, then
the time with both hoses must be smaller than +4+ hrs
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Suppose the time with both hoses was +3+ hrs, then
+1%2F8+%2B+1%2Ft+=+1%2F3+
Multiply both sides by +24t+
+3t+%2B+24+=+8t+
+5t+=+24+
+t+=+4.8+
This is much less than +8+ hrs ( small hose ), so the
2nd hose must be larger.
Hope this helps

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

The statement of the problem is misleading; but your solution is fine.

Think of it this way, without getting into the details of the mathematical solution:

If using two hoses fills the pool in exactly half the time that one hose alone takes, then the two hoses are doing the same amount of the work, which means they are working at the same rate....