A water tank has 8 pipes in total. Some are filling pipes and the rest are drainage pipes. Each filling pipe can fill 1/12 of the tank per hour, while each drainage pipe can empty 1/36 of the tank per hour. When all pipes are opened simultaneously, an empty tank gets filled in 3 hours. How many drainage pipes are there?

Question

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Let's denote the number of filling pipes as x, which means the number of drainage pipes is (8-x).

When we look at the hourly rates:
- x filling pipes collectively fill x/12 portion of the tank per hour
- (8-x) drainage pipes collectively empty (8-x)/36 portion of the tank per hour

The net filling rate equals the rate at which the tank is filled minus the rate at which it is emptied. Since the tank gets filled in 3 hours, the net filling rate must be 1/3 of the tank per hour.

Therefore, we can write the equation:
x/12 - (8-x)/36 = 1/3

To solve this equation, let's first find a common denominator for the left side:
x/12 - (8-x)/36 = x/12 - (8-x)/(3×12) = (3x)/36 - (8-x)/36 = (3x-8+x)/36 = (4x-8)/36

Now, our equation is:
(4x-8)/36 = 1/3

Multiplying both sides by 36:
4x-8 = 36 × (1/3) = 12

So:
4x = 20
x = 5

Therefore, the number of filling pipes is 5, and the number of drainage pipes is (8-5) = 3.

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