# Two identical taps fill 2/5 of a tank in 20 minutes

1. Apr 5, 2010

### mgb_phys

So a particularly dumb client has decided that before I can work for them I have to pass a high school maths test.
Never having had to do US school tests I looked at some practice questions, including:

"Two identical taps fill 2/5 of a tank in 20 minutes. When one of the taps goes dry in how many minutes will the remaining one tap fill the rest of the tank ?"

Brilliantly ambiguous question
If they mean that two taps together have filled 2/5 (40%) of the tank in 20mins, then each fills 20% in 20mins, ie 1%/min and so one will take 60mins to fill the remaining 60%.

If they mean that each of the taps alone fill 2/5 (40%) in 20mins, then each fills 2%/min and then one will fill the remaining 20% in 10min.

Or if you assume they are connected to the same water supply so that when one stops the other doubles in flow then you have either 30mins or 5mins.

The 'correct' answer apparently is 15mins?

2. Apr 6, 2010

### rs1n

I also like how a single tap can fill 3/5 of a tank faster (in allegedly 15 minutes) than two taps filling up only 2/5 of a tanks (20 minutes).

You might be better of not working with said client... I'd hate for them to claim they paid you enough when in fact, they had not :S -- and their contract is as ambiguous as the problem.

3. Apr 6, 2010

### Mentallic

No wonder why maths is hard!

4. Apr 6, 2010

5. Apr 6, 2010

### mgb_phys

Apparently this is test (GMAT) used by US schools to decide who does an MBA!
That would certainly explain a lot about the recent events on wall St.

6. Apr 6, 2010

### snshusat161

Is this question anyway related to Bernoulli's principle

7. Apr 6, 2010

### Cilabitaon

Bernoulli's wouldn't have too great an effect on the system; it's water.

8. Apr 6, 2010

### snshusat161

but I've read that bernoulli's theorem works best with low viscous liquid like water.

9. Apr 6, 2010

### mgb_phys

Since it's a multiple choice question supposedly aimed at testing the mental arithmetic of MBA students I'm guessing that non-linear computation fluid dynamics effects aren't a major consideration.

However I'm guessing that idiots setting this are basing their selection on "the computer says C so that mist be right - it's a computer".

If anyone has read Neal Stephenson's Cryptomnicon there is a brilliant example of this. The hero joins the navy and is set a simple ferryman problem as an IQ test - he assumes it can't be that simple and spends the entire exam developing a totally new theory of calculus of fluid flows.
Because he didn't answer any question he is graded F and sent to play in a band, arriving at Pearl Harbor just as his paper appears in the maths journal.

10. Apr 6, 2010

### snshusat161

Yeah. In my view you are very correct but I'm surprised that how none of them can figure it out. It's not only your book but I've seen this question with the same answer You've told in many websites, even those tutorial websites which have a very high reputation.

But for all those who wants to have some exercise of their brain, I've a question for You. Try to solve this question without using any knowledge of Physics. You'll find it very interesting.

"Three students are standing in a queue. A person came with a box containing two black hats and three white hats. He randomly put hats on their head and asked the students not to turn back neither to look up for the hat color. Now he started asking from the guy at the back for the color of the hat on his head but he can’t answer, then he asked from the second but he also can’t answer and when he asked from the next student (who was in the front of the queue), he answered correctly with complete explanation. Now think you are that student and I’m expecting the same answer from You."

11. Apr 6, 2010

### lanedance

white

12. Apr 6, 2010

### snshusat161

used probability? Tell me how you've made this conclusion.

13. Apr 7, 2010

### lanedance

3rd guy doesn't know what he is, so both in front can't have B (black), giving options:
1st W W B
2nd W B W
3rd ?
If 1st was B, then 2nd would know he is W... means 1st guy must be W

14. Apr 7, 2010

### snshusat161

lanedance, You really have a very high IQ level. I took about half an hour of constant thinking to solve this problem. How much time you took? According to my estimate you have solved this riddle in less than 5 minutes. Do you have heard this riddle before I've posted?

15. Apr 7, 2010

### Mentallic

I've heard of another variation to this.
But as future reference, if someone is giving you a riddle to solve, surely they would have heard about it and solved it beforehand.

16. Apr 8, 2010

### willem2

My guess is that they meant this and accidentally divided by 2 instead of multiplying.