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?
- 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?
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- Pipes A, B and C are attached to an empty cistern. While the first two can fill the cistern in 4 and 10 hours, respectively, the third can drain the cistern, when filled, in 6 hours. If all the three pipes are opened simultaneously when the cistern is half-full, how many hours will be needed to fill the cistern?
- Two pipes A and B can fill an empty cistern in 18 and 27 hours, respectively. Pipe C can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty Pipe A and Pipe C were turned on. After a few hours Pipe A was turned off and Pipe B was turned on instantly. In all, it took 55 hours to fill the cistern. For how many hours was Pipe B turned on?
- A pipe can fill a sump with water in 2 hours. Because of a leak, it took $2 \frac{1}{3}$ hours to fill the sump. The leak can drain all the water of the sump in:
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?
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?
Pipe J can fill a tank in 48 hours and pipe K can fill the same tank in 72 hours. If both the pipes are opened alternately for one hour each and pipe K is opened for the first hour, then in how much time the tank will be full?
