SOLUTION: One pipe alone can fill a tub in 12 minutes. Another pipe can fill it in only 8 minutes. How long would it take both piper to fill the tub

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Question 1204194: One pipe alone can fill a tub in 12 minutes. Another pipe can fill it in only 8 minutes. How long would it take both piper to fill the tub
Found 6 solutions by math_tutor2020, ikleyn, josgarithmetic, Alan3354, greenestamps, Edwin McCravy:
Answer by math_tutor2020(3817)   (Show Source):
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Let's say the tub has a capacity of 12*8 = 96 gallons.
The capacity doesn't matter and you can pick any number you want.

Pipe A fills the tub in 12 minutes when working alone.
Its unit rate is 96/12 = 8 gallons per min.

Pipe B fills the tub in 8 minutes when working alone.
Its unit rate is 96/8 = 12 gallons per min.

The combined unit rate of both pipes is 8+12 = 20 gallons per min.
This assumes neither pipe hinders the other.

The two pipes have a combined rate of 20 gallons per minute, and their task is to fill 96 gallons.
time = (amount done)/(rate)
time = 96/20
time = 4.8 minutes
time = 4 min + 0.8 min
time = 4 min + (0.8*60) sec
time = 4 min + 48 sec

Or we could have this conversion
4.8 min = 4.8*60 = 288 seconds

Answer by ikleyn(52911)   (Show Source):
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.
One pipe alone can fill a tub in 12 minutes. Another pipe can fill it in only 8 minutes.
How long would it take both piper to fill the tub
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First pipe makes of the job per minute. Second pipe makes of the job per minute. Two pipes working together make = = of the job per minute. It means that two pipes will make the entire job in minutes = minutes = 4 minutes and 48 seconds.

Solved.

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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
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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.

Answer by josgarithmetic(39630)   (Show Source):
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for unit of speed or fill rate

(Notice that one speed is two thirds the other speed.)

Both pipes working together, the sum of the individual speeds.

This is 24 minutes for 5 tubs.

, for time to fill 1 tub.
about 4 minutes 48 seconds

Answer by Alan3354(69443)   (Show Source):
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One pipe alone can fill a tub in 12 minutes. Another pipe can fill it in only 8 minutes. How long would it take both piper to fill the tub
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8*12/(8+12) = 96/20 = 4.8 minutes
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Not every simple problem is worth a Master's Thesis.

Answer by greenestamps(13215)   (Show Source):
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All of the responses you have received, if they show you how to solve the problem at all, use a variation of the standard setup:

where 1/12 is the fraction of the job one pipe does, 1/8 is the fraction the other pipe does, and 1/x is the fraction of the job they do together.

Here is an alternative method for solving this kind of "working together" problems.

Consider the least common multiple of the two given times, which is 24 minutes.

In 24 minutes, the first pipe could fill the tub 24/12 = 2 times and the second pipe could fill it 24/8 = 3 times.

So together in 24 minutes the two pipes could fill the tub 5 times; that means the time required to fill the tub once is 24/5 minutes, or 4 4/5 minutes, or 4 minutes 48 seconds.

Answer by Edwin McCravy(20065)   (Show Source):
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Here's the easy way. The Least Common Multiple method. LCM(12,8) = 24 The 1st pipe can fill 1 tub in 12 minutes, or 2 tubs in 24 minutes. The 2nd pipe can fill 1 tub in 8 minutes, or 3 tubs in 24 minutes. Therefore both pipes together can fill 5 tubs in 24 minutes. Therefore both pipes together can fill 1 tub in 24/5 minutes or 4 minutes 48 seconds. Look, mom, no algebra! J Edwin