A tank with a capacity of 7200 litres is filled by tap A in 9 minutes and by tap B in 12 minutes. Tap C can empty the tank in 6 minutes. What capacity of water is put in by A in one minute? What capac

Tap A fills 7200 litres in 9 minutes.

$$\text{Rate of A} = \frac{\text{Total capacity}}{\text{Time taken by A}} = \frac{7200 \text{ litres}}{9 \text{ minutes}}$$ $$\text{Rate of A} = 800 \text{ litres/minute}$$

Tap A puts 800 litres into the tank in one minute.

$$\boxed{800 \text{ litres}}$$

Tap B fills 7200 litres in 12 minutes.

$$\text{Rate of B} = \frac{\text{Total capacity}}{\text{Time taken by B}} = \frac{7200 \text{ litres}}{12 \text{ minutes}}$$ $$\text{Rate of B} = 600 \text{ litres/minute}$$

Tap B puts 600 litres into the tank in one minute.

$$\boxed{600 \text{ litres}}$$

Tap C empties 7200 litres in 6 minutes.

$$\text{Rate of C} = \frac{\text{Total capacity}}{\text{Time taken by C}} = \frac{7200 \text{ litres}}{6 \text{ minutes}}$$ $$\text{Rate of C} = 1200 \text{ litres/minute}$$

The net rate is the sum of filling rates minus the emptying rate.

$$\text{Net rate} = \text{Rate of A} + \text{Rate of B} - \text{Rate of C}$$ $$\text{Net rate} = 800 \text{ litres/minute} + 600 \text{ litres/minute} - 1200 \text{ litres/minute}$$ $$\text{Net rate} = 1400 \text{ litres/minute} - 1200 \text{ litres/minute}$$ $$\text{Net rate} = 200 \text{ litres/minute}$$

$$\text{Time} = \frac{\text{Total capacity}}{\text{Net rate}}$$ $$\text{Time} = \frac{7200 \text{ litres}}{200 \text{ litres/minute}}$$ $$\text{Time} = 36 \text{ minutes}$$

It will take 36 minutes to fill the tank if all taps are left open at the same time.

$$\boxed{36 \text{ minutes}}$$