Pipe Filling Time Calculation
This problem involves calculating the combined time taken for multiple pipes to fill a tank, given their individual filling times.
Individual Pipe Rates
- Pipe A fills the tank in 18 hours. Its rate is $\frac{1}{18}$ of the tank per hour.
- Pipe B fills the tank in 28 hours. Its rate is $\frac{1}{28}$ of the tank per hour.
- Pipe C fills the tank in 11 hours. Its rate is $\frac{1}{11}$ of the tank per hour.
Combined Filling Rate
When pipes operate together, their rates add up. The combined rate is:
$ \text{Rate}_{\text{combined}} = \text{Rate}_{\text{A}} + \text{Rate}_{\text{B}} + \text{Rate}_{\text{C}} $ $ \text{Rate}_{\text{combined}} = \frac{1}{18} + \frac{1}{28} + \frac{1}{11} $To add these fractions, find a common denominator. The Least Common Multiple (LCM) of 18, 28, and 11 is 2772.
$ \text{Rate}_{\text{combined}} = \frac{154}{2772} + \frac{99}{2772} + \frac{252}{2772} $ $ \text{Rate}_{\text{combined}} = \frac{154 + 99 + 252}{2772} = \frac{505}{2772} \text{ tank per hour} $Combined Filling Time
The time taken to fill the tank together is the reciprocal of the combined rate:
$ \text{Time}_{\text{combined}} = \frac{1}{\text{Rate}_{\text{combined}}} $ $ \text{Time}_{\text{combined}} = \frac{1}{\frac{505}{2772}} = \frac{2772}{505} \text{ hours} $Convert to Mixed Fraction
To express this improper fraction as a mixed number:
$ \frac{2772}{505} = 5 \text{ with a remainder of } 2772 - (5 \times 505) = 2772 - 2525 = 247 $Therefore, the time taken is $5\frac{247}{505}$ 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 12 hours, pipe B can fill the same tank in 22 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 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:
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?
Pipes A, B and C can together fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B together fill the remaining part in 7 hours. The time taken (in hours) by C alone to fill the tank is:
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?
