Calculating Combined Pipe Filling Time
This problem involves finding the time it takes for multiple pipes operating simultaneously to fill a tank, given their individual filling times.
Individual Pipe Rates
First, determine the rate at which each pipe fills the tank. The rate is the fraction of the tank filled per hour.
- Rate of Pipe A: $\frac{1}{19}$ tank per hour.
- Rate of Pipe B: $\frac{1}{21}$ tank per hour.
- Rate of Pipe C: $\frac{1}{8}$ tank per hour.
Combined Rate Calculation
To find the combined rate when all pipes operate together, add their individual rates.
Combined Rate = Rate A + Rate B + Rate C
Combined Rate = $\frac{1}{19} + \frac{1}{21} + \frac{1}{8}$
Find a common denominator, which is the least common multiple (LCM) of 19, 21, and 8. LCM(19, 21, 8) = $19 \times 21 \times 8 = 3192$.
Combined Rate = $\frac{1 \times (21 \times 8)}{19 \times 21 \times 8} + \frac{1 \times (19 \times 8)}{19 \times 21 \times 8} + \frac{1 \times (19 \times 21)}{19 \times 21 \times 8}$
Combined Rate = $\frac{168}{3192} + \frac{152}{3192} + \frac{399}{3192}$
Combined Rate = $\frac{168 + 152 + 399}{3192} = \frac{719}{3192}$ tank per hour.
Total Time Calculation
The time taken to fill the tank together is the reciprocal of the combined rate.
Time = $\frac{1}{\text{Combined Rate}}$
Time = $\frac{1}{\frac{719}{3192}} = \frac{3192}{719}$ hours.
Convert to Mixed Fraction
Convert the improper fraction $\frac{3192}{719}$ into a mixed number.
Divide 3192 by 719:
$3192 \div 719 = 4$ with a remainder of $3192 - (4 \times 719) = 3192 - 2876 = 316$.
Therefore, the time taken is $4 \frac{316}{719}$ hours.
Similar Questions
- 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 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 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?
- 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?
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- 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:
- Pipes A and B are fitted to a tank. A is the filling pipe and B can be used for filling or emptying at the same rate. When B is used for filling, it takes time 't' along with A to fill the tank. If it is used for emptying when A is filling the tank, the time taken for the tank to fill up would be '5t'. Find the ratio of the rates of A and B.
- 28 pipes are connected to a tank. Some of them pour water into the tank, whereas the rest drain water out of it. Each of the pipes that fill water can fill the empty tank in 14 hours, whereas any of the drainpipes can empty the filled tank in 35 hours. If all the pipes are opened simultaneously when the tank is empty and the tank is filled in 2.5 hours, how many of the pipes were drainpipes?
Important Questions from Pipe and Cistern
A pipe can fill a cistern in 20 minutes where as the cistern when full can be emptied by a leak in 28 minutes. When both are opened, The time taken to fill the cistern is:
‘A’ pipe can empty a tank in 20 minutes. The second pipe ‘B’ has a diameter twice as that of ‘A’. If both A & B pipe are attached to the tank how much time will be required to empty the tank?
Pipes A and B can empty a full tank in 16 hours and 24 hours, respectively. Pipe C alone can fill the empty tank in 4 hours. If A, B and C are opened together, the tank will be 35% full after :
Pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Both these pipes were opened simultaneously. After 20 minutes, a leak at the bottom of the tank was spotted which was immediately sealed. The tank was full in another 15 minutes. The leak alone can empty the full tank in:
A cistern has a leak which would empty it in 6 hours. A tap is turned on which admits 10 litres of water per minute into the cistern. When it is full it is now emptied in 10 hours. What is the capacity (in litres) of the cistern?
