Question 446383: If Jill fills a pool with water in 30 min, jack fills a pool with water in 45 min and John fills a pool with water in 1 hour and 30 min. How long will it take if they work together.
Found 5 solutions by stanbon, mananth, ikleyn, greenestamps, math_tutor2020:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If Jill fills a pool with water in 30 min, jack fills a pool with water in 45 min and John fills a pool with water in 1 hour and 30 min. How long will it take if they work together.
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Jill rate = 1/30 job/min
Jack rate = 1/45 job/min
John rate = 1/90 job/min
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Together rate = 1/x job/min
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Equation:
rate + rate + rate = together rate
1/30 + 1/45 + 1/90 = 1/x
Multiply thru by 90x to get:
3x + 2x + x = 90
6x = 90
x = 15 minutes (time to fill the pool working together)
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Cheers,
Stan H.
Answer by mananth(16949)  (Show Source):
You can put this solution on YOUR website! Filling the pool is 1 job
Jill 0.5 hours
It does 2 jobs in 1 hours
Jack 0.75 hours
It does 1 1/ 3 of thejob in 1 hours
John 1.5 hours
It does 2/3 of the job in 1 hours
Together they will do 2 + 1.33 + 0.67
Together they will do 4 of the job in one hours
So they will take 1/4 hours
So they will take 0.25 hours
Answer by ikleyn(53430)  (Show Source):
Answer by greenestamps(13258)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the standard algebraic method shown by the other tutor. This method works especially well in this particular problem because the numbers are "nice".
The three times for the three people to fill the pool, in minutes, are 30, 45, and 90.
Consider the least common multiple of those times, which is 90 minutes. In 90 minutes, ...
Jill could fill the pool 90/30 = 3 times;
Jack could fill the pool 90/45 = 2 times; and
John could fill the pools 90/90 = 1 time
Therefore, in 90 minutes, the three of them could fill the pool 3+2+1 = 6 times.
And if they can fill the pool 6 times in 90 minutes, the time it takes them to fill the pool once is 90/6 = 15 minutes.
ANSWER: 15 minutes
Answer by math_tutor2020(3828) (Show Source):
You can put this solution on YOUR website!
Answer: 15 minutes
Reasoning
1 hr + 30 min = 60 min + 30 min = 90 min
When working alone we have these time durations in minutes only
Jill = 30 min
Jack = 45 min
John = 90 min
The LCM of that set is 90.
Consider a pool with a capacity of 9000 gallons. This hypoethical value can be changed to anything else and the final answer will be the same at the end.
I'm tacking a few zeros onto 90 to get some large capacity, so when we divide it later on we get integer results.
When working alone, Jill fills 9000 gallons in 30 min. Her rate is 9000/30 = 300 gallons per min.
rate = amountDone/time
When working alone, Jack does the same job in 45 min. His rate is 9000/45 = 200 gallons per min.
And when working alone, John's rate is 100 gallons per minute because 9000/90 = 100
The unit rates for each person are then added up. The assumption is that each person doesn't hinder the other when working together.
Eg: John doesn't slow down Jack
Jill + Jack + John = 300+200+100 = 600
They combine to a rate of 600 gallons per minute.
When working together, the pool gets filled in 15 minutes because (9000 gallons)/(600 gallons per min) = 15
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