SOLUTION: Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the cold water faucet 12 minutes to fill the tub by itself

Question 1100984: Left on together, the cold and hot water faucets of a certain bathtub take
4
minutes to fill the tub. If it takes the cold water faucet
12
minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub on its own?
Found 3 solutions by ikleyn, richwmiller, greenestamps:
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.

When both facets are turned on, they fill of the bathtub volume per minute. When only cold facet is turned on, it fills of the bathtub volume per minute. It means that the contribution of the hot facet is the difference - = - = = of the bathtub volume per minute. Therefore, it will take 6 minutes for the hot facet to fill the bathtub working alone.

Solved.

------------------------
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
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    - 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
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to your archive and use it when it is needed.

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the cold water faucet 12 minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub on its own?
1/h+1/12=1/4
1/h+1/12=3/12
1/h=2/12
1h=1/6
h=6 minutes for hot water to fill the tub on its own.
check
1/6+1/12=1/4
2/12+1/12=3/12=1/4
ok
Warning: I am still sick in bed. Double check my work.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

First the standard method of solution, usually taught in beginning algebra classes....

The two tubs together fill the tub in 4 minutes; so they fill 1/4 of the tub in 1 minute.

The cold water faucet fills the tub alone in 12 minutes; so it fills 1/12 of the tub in 1 minute.

So the fraction of the tub that the hot water faucet fills in 1 minute is

Since the hot water faucet can fill 1/6 of the tub in 1 minute, it can fill the tub in 6 minutes.

Algebraically, if x is the number of minutes is takes the hot water faucet to fill the tub alone,

And here is an alternative solution method which I find many students prefer....

The cold water faucet can fill the tub in 12 minutes.
In those same 12 minutes, the two faucets together could fill the tub 3 times.
But if together they can fill the tub 3 times in 12 minutes, and the cold water faucet alone can fill it only 1 time in 12 minutes, then the hot water faucet can fill the tub 2 times in 12 minutes.
But that means it can fill the tub once in 6 minutes.

Try both methods for solving this kind of problem and find which "workd' better for you.
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