Explanation:

Here’s how it shakes out:

- Pipe A fills the tank in 16 minutes. Its rate is 1/16 of the tank per minute.

- Pipe B empties it in 24 minutes. Its rate is -1/24 per minute (since it’s taking water out).

- If both are open, the combined rate per minute: (1/16) - (1/24) = (3-2)/48 = 1/48. So, together, they fill 1/48 of the tank each minute.

- Suppose B is open for x minutes, then closed for the rest. For x minutes, both work: they fill x/48 of the tank.

- For the remaining (30-x) minutes, only A works: it fills (30-x)/16 of the tank.

- The tank should be full at 30 minutes:

x/48 + (30 - x)/16 = 1

Multiply both sides by 48 for easier numbers:

x + 3(30 - x) = 48

x + 90 - 3x = 48

-2x = 48 - 90

-2x = -42

x = 21

Now comparing the options:

1. 21 minutes ? This is correct. B should be open for 21 minutes then closed, so A can finish filling the tank at 30 minutes.

2. 20 minutes (Too little, won’t fill the tank in time.)

3. 18 minutes (Leaves too much work for A.)

4. 15 minutes (A has to work too long alone to finish on time.)

5. 19 minutes (Still not enough with both working together.)