## viniterranova 4 years ago A tank has two taps that can fill it within 24 hours and 30 hours respectively, and a drain that empties in 16 hours. If we open simultaneously the whole set (two faucets and a drain), how time the tank will be filled?

1. JamesJ

The way to think of this and all problems like this is in terms of rates. The first tap fills 1/24th of a tank per hour; the second tap at a rate of 1/30. Therefore their combined rate is $$1/24 + 1/30$$. The drain drains the tank at a rate of 1/16. Therefore the combined rate of all three is $R = \frac{1}{24} + \frac{1}{30} - \frac{1}{16}$ Then the time required to fill the tank is $$1/R$$.

2. viniterranova

I have found 10,43 hours. Am i right?

3. JamesJ

What value do you have for R? 10.43 hours isn't right.

4. viniterranova

What is the right value?

5. JamesJ

As R = 1/24 + 1/30 - 1/16, just do the math. What value do you get for R?

6. JamesJ

put it in your calculator if you like.

7. JamesJ

I get R = 0.0125 = 1/80 . Hence the number of hours 1/R = ...

8. JamesJ

For the record, if there was no drain, then the two taps would fill the sink at a combined rate of 1/24 + 1/30 = 0.075 and therefore the sink would fill in 1/0.075 = 13.3 hours. Whatever answer you get with the drain, it had obviously better be longer than 13.3 hours.

9. viniterranova

I get 0,1249 for R.

10. viniterranova

So the righ answer is 80 hours.

11. JamesJ

R = 0.0125 and hence 1/R = 80 hours, yes.