A tank of capacity 9600 litres is filled by tap R in 9 minutes, tap S in 12 minutes and emptied by tap T in 6 minutes. What fraction of the tank is filled in 1 minute if R and S are opened?

Tap R fills 9600 litres in 9 minutes.

$$\text{Rate of R} = \frac{\text{Total capacity}}{\text{Time taken by R}} = \frac{9600 \text{ litres}}{9 \text{ minutes}}$$ $$\text{Rate of R} = 1066.67 \text{ litres/minute}$$

Tap R puts approximately 1066.67 litres into the tank in one minute.

$$\boxed{1066.67 \text{ litres}}$$

Tap T empties 9600 litres in 6 minutes.

$$\text{Rate of T} = \frac{\text{Total capacity}}{\text{Time taken by T}} = \frac{9600 \text{ litres}}{6 \text{ minutes}}$$ $$\text{Rate of T} = 1600 \text{ litres/minute}$$

Tap T draws 1600 litres from the tank in one minute.

$$\boxed{1600 \text{ litres}}$$

Tap S fills 9600 litres in 12 minutes.

$$\text{Rate of S} = \frac{\text{Total capacity}}{\text{Time taken by S}} = \frac{9600 \text{ litres}}{12 \text{ minutes}}$$ $$\text{Rate of S} = 800 \text{ litres/minute}$$

$$\text{Combined rate (R+S)} = \text{Rate of R} + \text{Rate of S}$$ $$\text{Combined rate (R+S)} = 1066.67 \text{ litres/minute} + 800 \text{ litres/minute}$$ $$\text{Combined rate (R+S)} = 1866.67 \text{ litres/minute}$$

Tap R and Tap S pour approximately 1866.67 litres into the tank in one minute.

$$\boxed{1866.67 \text{ litres}}$$

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

$$\text{Net rate} = \text{Rate of R} + \text{Rate of S} - \text{Rate of T}$$ $$\text{Net rate} = 1066.67 \text{ litres/minute} + 800 \text{ litres/minute} - 1600 \text{ litres/minute}$$ $$\text{Net rate} = 1866.67 \text{ litres/minute} - 1600 \text{ litres/minute}$$ $$\text{Net rate} = 266.67 \text{ litres/minute}$$

$$\text{Time} = \frac{\text{Total capacity}}{\text{Net rate}}$$ $$\text{Time} = \frac{9600 \text{ litres}}{266.67 \text{ litres/minute}}$$ $$\text{Time} = 36 \text{ minutes}$$

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

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