Understanding Pipe Rates
Let the rate at which pipe B fills the tank be \(R_B\) (tanks per minute).
Since pipe A fills three times as fast as pipe B, the rate of pipe A is \(R_A = 3 \times R_B\). The slower pipe is B.
Calculating Combined Rate
When both pipes work together, their rates add up. The problem states they fill the tank in 36 minutes.
Therefore, the combined rate is:
\( R_A + R_B = \frac{1 \text{ tank}}{36 \text{ minutes}} \)Solving for the Slower Pipe's Rate
Substitute the rate of pipe A (\(R_A = 3 R_B\)) into the combined rate equation:
\( (3 R_B) + R_B = \frac{1}{36} \)Combine the terms involving \(R_B\):
\( 4 R_B = \frac{1}{36} \)Solve for \(R_B\):
\( R_B = \frac{1}{4 \times 36} \) \( R_B = \frac{1}{144} \text{ tanks/minute} \)Determining Slower Pipe's Fill Time
The time taken for the slower pipe (B) to fill the tank alone is the reciprocal of its rate (\(R_B\)).
Time for Pipe B = \( \frac{1}{R_B} \)
Time for Pipe B = \( \frac{1}{1/144} \) minutes
Time for Pipe B = 144 minutes
Similar Questions
- Three pipes of diameters 2 cm, 3 cm and 4 cm are running together to fill a cistern. The smallest pipe alone can fill the cistern in 232 minutes. The amount of water flowing in each pipe is proportional to the square of its diameter. The time (in minutes) taken by all pipes running together to completely fill the cistern is:
- A cistern can be filled by a tap in 5 hours and emptied by an outlet pipe in 9 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?
- Two pipes, A and B, can fill a water tank in 1 hour and \(1\frac{1}{2}\) hours, respectively. Pipe A is opened. After 15 minutes without closing it, pipe B is also opened. How much more time will both the pipes take to fill the tank?
- A cistern has two inlets \(I_1\) and \(I_2\) which can fill it in 16 hours and 20 hours, respectively. An outlet can empty the full cistern in 12 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?
- Tap A can fill an empty swimming pool in 10 h. Tap B can fill it in 15 h. How much time will the two taps take to fill the empty pool together?
- Two taps can fill an empty cistern in 8 min and 20 min, respectively. However, together, they take 30 min to fill it because of a leak. How much time will the leak take to empty a full cistern?
- Hose A and B can fill a pool in 5 and 10 minutes respectively. After 2 minutes, hose B gets blocked. How much time will hose A take to fill the remaining pool?
- A certain type of taps can fill a tank in 10 hours each. If there is a leakage that can empty the full tank in 4 hours, then how many taps are required to fill the tank in 4 hours?
- Two taps can fill an empty cistern in 8 min and 20 min, respectively. However, together, they take 30 min to fill it because of a leak. How much time will the leak take to empty a full cistern?
- Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed, and P and Q can fill the remaining part in 7 hours. Find the number of hours taken by R alone to fill the tank.
Important Questions from Pipe and Cistern
Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely?
The compound interest on Rs. 64,000 for 3 years, compounded annually at 7.5% p.a. is
A water tank can be emptied in 40 minutes by a pipe of d 'diameter, so how long will it take for a 2d diameter pipe to be emptied?
A pipe can fill a tank in 4 hours, while a leak which is at one-fourth of the height of the tank from bottom can empty upto that part in 2 hours. If both are operated simultaneously and initially the tank is full, then when it will be one-fourth full?
Two pipes X and Y can fill an empty tank in 16 hours and 20 hours respectively. Pipe Z alone can empty the completely filled tank in 25 hours. Firstly both pipes X and Y are opened and after 6 hours pipe Z is also opened. What will be the total time (in hours) taken to completely fill the tank?
