SOLUTION: One pump fills a tank 3 times as fast as another pump. If the pumps work​ together, they fill the tank in 12 minutes. How long does it take for each pump to fill the​ tank?

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Question 1153927: One pump fills a tank 3 times as fast as another pump. If the pumps work​ together, they fill the tank in 12 minutes. How long does it take for each pump to fill the​ tank?
Found 4 solutions by ramkikk66, josgarithmetic, greenestamps, ikleyn:
Answer by ramkikk66(644) About Me  (Show Source):
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This problem may seem puzzling at first since the actual rate of filling, and the actual capacity of the tank are not given. However it can be solved as follows.
Let vol of tank be X litres
Let rate of P1 be y litres/min
Then rate of P2 is 3%2Ay litres/min
If they work together, rate is 4%2Ay litres /min
and it takes 12 min.
So capacity of tank = 4%2Ay+%2A+12+=+48%2Ay litres
So if P1 alone is used, time taken
= 48%2Ay+%2F+y+=+48+min
If P2 alone is used, time taken
= %2848%2Ay%29+%2F+%283%2Ay%29+=+16+min
Solved.

Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
PUMP                 RATE in TANKS/MINUTES

One pump              3/x

Another pump          1/x

Combined             1/12

3%2Fx%2B1%2Fx=1%2F12---------------solve.
-
4%2Fx=1%2F12
x%2F4=12%2F1
highlight%28x=48%29-----------minutes for the "another pump" working alone
highlight%2816%29------------minutes for the "one pump" working alone

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Since the faster pump works 3 times as fast as the slower, in filling the tank the faster pump does 3/4 of the work and the slower pump does 1/4.

The faster pump fills 3/4 of the tank in 12 minutes; the time it would take that pump alone to fill the tank is 12*(4/3) = 16 minutes.

The slower pump fills 1/4 of the tank in 12 minutes; the time it would take that pump alone to fill the tank is 12*4 = 48 minutes.

ANSWERS:
Faster pump alone: 16 minutes
Slower pump alone: 48 minutes

Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given that that first (the faster) pump works as effectively as three slower pumps.


Therefore, you may think that 4 = 3+1 slower pumps, actually, work, and these 4 pumps fill the tank in 12 minutes.


Hence, one single slower pump can fill the tank in 4*12 = 48 minutes, working alone.


Next, since the faster pump is 3 times as fast, it needs only 48/3 = 16 minutes to fill the tank, working alone.

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
    - 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.