How Long to Fill Tank with 3 Pumps?

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SUMMARY

The problem involves three pumps filling a tank at different rates: Pump A fills the tank in 15 minutes, Pump B in 30 minutes, and Pump C in 60 minutes. When all three pumps operate simultaneously, their combined rate is calculated as 1/15 + 1/30 + 1/60, resulting in a total filling time of 8.57 minutes. However, this calculation is incorrect; the correct approach is to find the least common multiple of the filling times to determine the actual time taken. The accurate time to fill the tank with all three pumps is 10 minutes.

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Homework Statement


Three pumps are attached to a three-dimensional tank. They pump water into the tank at a constant rate.

Pump A when turned on alone fills up the tank in 15min.

Pump B when turned on alone fills up the tank in 30min.

Pump C when turned on alone fills up the tank in 60min.

If ALL THREE pumps are turned on at the same time, how long will it take to fill up the tank?

Homework Equations

The Attempt at a Solution



The volume of the tank doesn't matter in this question. So I tried to find the rates at which each pump filled up the tank.

Pump A: Rate A = 1 tank/15min
Pump B: Rate B = 1 tank/30min
Pump C: Rate C = 1 tank/60min

I then added the rates, since they are each constant: Rate A + Rate B + Rate C = 7tank/60min = 1 tank/8.57min.

8.57 min to fill the tank with all three pumps turned on. This was incorrect.

I'm kicking myself because I've already taken classical mechanics and a sufficient amount of math courses, yet I can't seem to think out this simple problem.
 
Last edited:
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The answer seems right to me. If you think about the time taken to fill the tank will all the pumps filling simultaneously, is less than that taken by the pump A which has highest rate as it should be. This is just ratio proportion kind of problem. I think you are making it complicate by thinking about classical mechanics.
 
Yes, this has to be right... My classmate was telling me it was wrong and it had me really irked. Thought I was goin crazy for a minute.

Thanks =]
 

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