Pipe Filling Rates Calculation
First, we determine the rate at which each pipe fills the tank per hour:
- Pipe A's rate: $\frac{1}{12}$ of the tank per hour.
- Pipe B's rate: $\frac{1}{22}$ of the tank per hour.
- Pipe C's rate: $\frac{1}{8}$ of the tank per hour.
Combined Pipe Rate Determination
To find the combined rate when all pipes operate together, we add their individual rates:
Combined Rate = Rate A + Rate B + Rate C
Combined Rate = $\frac{1}{12} + \frac{1}{22} + \frac{1}{8}$
To add these fractions, we find the least common multiple (LCM) of the denominators (12, 22, and 8). The LCM is 264.
Combined Rate = $\frac{1 \times 22}{12 \times 22} + \frac{1 \times 12}{22 \times 12} + \frac{1 \times 33}{8 \times 33}$
Combined Rate = $\frac{22}{264} + \frac{12}{264} + \frac{33}{264}$
Combined Rate = $\frac{22 + 12 + 33}{264} = \frac{67}{264}$ of the tank per hour.
Total Time Calculation
The total time taken to fill the tank is the reciprocal of the combined rate:
Time = $\frac{1}{\text{Combined Rate}}$
Time = $\frac{1}{\frac{67}{264}} = \frac{264}{67}$ hours.
To express this as a mixed number:
$264 \div 67 = 3$ with a remainder of $63$.
Therefore, the time taken is $3 \frac{63}{67}$ hours.
Similar Questions
- Two pipes can fill a cistern, individually, in 36 min and 45 min, respectively. There is a pipe located at the bottom of the cistern to empty it. If all the three pipes are opened simultaneously, then the empty cistern gets filled in 70 min. How long will the pipe at the bottom of the tank take to empty the completely filled cistern if no other pipe is then open?
- 6 pipes, all of same type, are required to fill a tank in 1 h 20 min. How long will it take if only 5 pipes of the same type are used?
- An inlet pipe can fill a tank in 4 h and an outlet pipe can empty the tank in 6 h. By mistake, both the pipes are kept open. Find the number of hours in which the tank will be half-full.
- Tap A can fill a tank in 6 h, whereas Tap B can fill it in 8 h. Tap C can empty the same tank in 4 h. If all the taps are opened together, how long will it take to fill the tank?
- Pipe 1 can empty a tank in 6 h while pipe 2 can do so in 18 h. If both are working together, in how much time will they empty the full tank?
- Tap A can fill a tank in 40 min and Tap B can empty the tank in 60 min. If the taps are opened at the same time, then the time taken to fill the tank will be:
- Pipe A can fill a tank in 19 hours, pipe B can fill the same tank in 21 hours and pipe C can fill the same tank in 8 hours. The time taken by them to fill the same tank if they operate together is:
- Pipe A can fill a tank in 18 hours, pipe B can fill the same tank in 28 hours and pipe C can fill the same tank in 11 hours. The time taken by them to fill the same tank if they operate together is:
Two taps can fill a cistern in 4 hours and 9 hours, respectively. A third tap can empty it in 9 hours. How long (in hours) will it take to fill one-fourth of the empty cistern if all the taps are opened together?
A cistern is filled by two taps, C and D, in 54 minutes and 81 minutes, respectively. There is also a drain E at the bottom. If all three are opened simultaneously, the cistern is filled in 108 minutes. In how many minutes can drain E alone empty the cistern? (up to two decimal places)
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?
