Pipe Emptying Rate Calculation
First, determine the rate at which each pipe empties the tank individually.
- Pipe 1 empties the full tank in 6 hours. Its rate is $\frac{1}{6}$ of the tank per hour.
- Pipe 2 empties the full tank in 18 hours. Its rate is $\frac{1}{18}$ of the tank per hour.
Combined Pipe Emptying Rate
When both pipes work together, their rates add up.
Combined rate = Rate of Pipe 1 + Rate of Pipe 2
Combined rate = $\frac{1}{6} + \frac{1}{18}$
To add these fractions, find a common denominator, which is 18.
Combined rate = $\frac{1 \times 3}{6 \times 3} + \frac{1}{18} = \frac{3}{18} + \frac{1}{18}$
Combined rate = $\frac{3+1}{18} = \frac{4}{18}$
Simplify the combined rate:
Combined rate = $\frac{2}{9}$ of the tank per hour.
Combined Time Calculation
The time taken to empty the tank when working together is the reciprocal of the combined rate.
Time = $\frac{1}{\text{Combined Rate}}$
Time = $\frac{1}{\frac{2}{9}}$
Time = $\frac{9}{2}$ hours
Convert this improper fraction to a decimal or mixed number:
Time = $4.5$ hours
Therefore, if both pipes work together, they will empty the full tank in 4.5 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?
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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
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