A tank has three taps. The first can fill the tank in 4 hours, the second can fill the tank in 2 hours and the third can empty the tank in 8 hours. How long will it take to fill the tank with all three taps operating at the same time? (You can assume the tank is empty to begin with).
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7 comment(s):
This is not a puzzle, it's simple arithmetic.
Arithmetic is the oldest branch of mathematics. Mathematical problems can be puzzles. So, this is a puzzle.
This is indeed not just simple arithmetic.
It might be, if we took it at face-value, but in the real world, it's not so simple. If we assume that tap 3 is tapped directly into the bottom of the tank, let us look at tap 3. I'd assume a proponent of simple arithmetic would assign a steady rate of 1/8 tank per hour, 1/32nd per quarter hour.
Oh, if only real life were so easy.
Nobody tells us the depth of the tank, but simple observation will show that the water issuing from tap 3 will issue considerably more vigourously when the tank is filled to the brim, less so when the depth is just a few millimetres.
With time and observation of the tank's characteristics, we could draw a curve.
Perhaps the tank is a simple cube? or conical? they might well have widely differing emptying behaviour. A conical bottomed tank, with the water swirling, vs a cubic, flat-bottomed tank with random eddies?
And we're not onto the filling taps yet.
Are they tapped off the same main? pump or gravity fed?
What are the flow characteristics of the pipework?
It's entirely possible that, if they're on the same pipe, that the two-hour rate is the maximum the pipe can carry, and that opening both taps will give no advantage.
Disclaimer here: In part of my professional life, flow-rates in pipework are exactly what I do, what I must calculate, design for, predict, and test.
Not long ago, I was working on a very similar problem involving a tank 25 metres above the ground, feeding a fire-sprinkler system in industrial premises.
I had to figure out if the existing town main could fill it faster than it was capable of flowing out, if not, then what sizes of pipes and boost pumps would be needed to refill from an underground reservoir, and how these rates might be affected when fire-crews started taking hose pressure from the town main.
Simple arithmetic? Well, it can be, if we just assume steady-state behaviour. But the real world's not so simple.
So my answer to the question? "It depends on a lot of things we don't yet know."
gerard, would you think "13+22-5" qualifies as a puzzle? Because that's what this is, only with rational numbers instead of natural ones.
soubriquet, the problem is formulated in such a way that we can safely assume the system is set up in such a (complicated) manner that it does indeed enable constant flow, both incoming and outgoing, irrespective of any fluctuations in fluid pressure. I'm sure the current state of the art allows for such solutions.
With all due respect, I beg to differ.
The question is given in such a way that we cannot safely assume constant flow.
That's the thing that used to drive me crazy about school arithmetic problems, the questions were composed in such a loose, and often ambiguous character that they were unworkable in the real world.
For instance, if one man can dig a hole two feet square by four feet deep, in two hours, how long would it take two men?
Well, I'd say, if little Tommy Dolan were to dig it, he'd be done in much less than an hour. In two hours he'd have barrowed the dirt away, swept the site and gone off to the next task.
But let's pretend we have two identically equipped diggers, twins, each capable, in this homogenous earth, of the two-hour rate. How long will it take them both to dig the same hole?
The answer is either two hours, or much longer. If one alone digs, the two hour rate stands, but if both try to dig, they barely fit in the hole, and hinder each other's movements, thus turning the job into a nightmare.
To clarify, if we start with just numbers, and ask a purely number question, it's simply arithmetic, but if we phrase it as a real world question, we should not rule out real world answers.
soubriquet (above) said what my brain was trying to think about...it's not a simple math problem, instead a complicated physics problem. Interesting though.
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