What is the formula to calculate the time taken to fill a cistern using multiple pipes?

The formula to find the total time taken to fill a cistern using multiple pipes is: 1/(1/r₁ + 1/r₂ + ... + 1/rₙ), where r₁, r₂, ..., rₙ are the rates of each pipe.

If Pipe A can fill a cistern in 4 hours and Pipe B can fill it in 6 hours, how long will it take for both pipes to fill the cistern together?

First, find the rates: r₁ = 1/4 and r₂ = 1/6. The combined rate is 1/(1/4 + 1/6) = 1/(3/12 + 2/12) = 1/(5/12) = 12/5 hours or 2.4 hours.

A cistern is filled by Pipe A in 8 hours and emptied by Pipe B in 12 hours. What is the net rate when both pipes are open?

The rates are: Pipe A = 1/8 and Pipe B = 1/12. The net rate = 1/8 - 1/12 = (3/24 - 2/24) = 1/24. Thus, the net rate is 1/24 cisterns per hour.

If a cistern can be filled by Pipe A in 10 hours and emptied by Pipe B in 20 hours, how long will it take to fill the cistern with both pipes open?

Rate of Pipe A = 1/10 and Pipe B = 1/20. The net rate is 1/10 - 1/20 = (2/20 - 1/20) = 1/20. Therefore, it will take 20 hours to fill the cistern.

How do you calculate the time taken to fill a cistern if one pipe is filling it and another is emptying it?

Use the formula: Time = 1/(Rate of filling - Rate of emptying). Ensure the rates are in the same units (e.g., cisterns per hour).

A cistern is filled by Pipe A in 5 hours and Pipe B fills it in 3 hours. If both pipes are opened for 1 hour, how much of the cistern is filled?

In 1 hour, Pipe A fills 1/5 and Pipe B fills 1/3. Together, they fill (1/5 + 1/3) = (3/15 + 5/15) = 8/15 of the cistern.

If Pipe A can fill a cistern in 6 hours and Pipe B in 9 hours, how long will it take both pipes to fill the cistern if they work together?

The combined rate = 1/6 + 1/9 = (3/18 + 2/18) = 5/18. Thus, the time taken is 18/5 hours or 3.6 hours.

A cistern is being filled by two pipes, A and B, which can fill it in 4 hours and 6 hours, respectively. If both pipes are opened for 2 hours, how much of the cistern is filled?

In 2 hours, Pipe A fills (2/4) = 1/2 and Pipe B fills (2/6) = 1/3. Together, they fill (1/2 + 1/3) = (3/6 + 2/6) = 5/6 of the cistern.

If Pipe A can fill a cistern in 8 hours and Pipe B can empty it in 10 hours, how long will it take to fill the cistern with both pipes open?

The filling rate of A is 1/8 and the emptying rate of B is 1/10. The net rate is 1/8 - 1/10 = (5/40 - 4/40) = 1/40. Therefore, it will take 40 hours to fill the cistern.

How do you determine the time taken to fill a cistern if both filling and emptying pipes are working?

The time taken is calculated as Time = 1/(Rate of filling - Rate of emptying). Remember to use rates in the same units.

A cistern can be filled by Pipe A in 15 hours and emptied by Pipe B in 10 hours. What is the net rate if both are open?

Rate of A = 1/15 and Rate of B = 1/10. The net rate = 1/15 - 1/10 = (2/30 - 3/30) = -1/30. This means the cistern will be emptied.

If Pipe A fills a cistern in 7 hours and Pipe B fills it in 14 hours, how long will they take together?

Combined rate = 1/7 + 1/14 = (2/14 + 1/14) = 3/14. Thus, the time taken is 14/3 hours or approximately 4.67 hours.

A cistern is filled by Pipe A in 5 hours and emptied by Pipe B in 15 hours. If both are open, how much of the cistern is filled in 1 hour?

Rate of A = 1/5 and rate of B = 1/15. The net rate = 1/5 - 1/15 = (3/15 - 1/15) = 2/15. Therefore, 2/15 of the cistern is filled in 1 hour.

If Pipe A can fill a tank in 9 hours and Pipe B can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened for 3 hours?

In 3 hours, Pipe A fills (3/9) = 1/3 and Pipe B fills (3/6) = 1/2. Together, they fill (1/3 + 1/2) = (2/6 + 3/6) = 5/6 of the tank. 1/6 remains.

A cistern can be filled by Pipe A in 12 hours and emptied by Pipe B in 18 hours. How long will it take to fill the cistern with both pipes open?

Rate of A = 1/12 and Rate of B = 1/18. The net rate = 1/12 - 1/18 = (3/36 - 2/36) = 1/36. Therefore, it will take 36 hours to fill the cistern.