Calculating Combined Tank Filling Time
This problem involves calculating the time taken to fill a tank when one tap fills it and another simultaneously empties it. We need to find the net filling rate.
Step 1: Determine Individual Rates
- Tap A fills the tank in 40 minutes. Its filling rate is $ \frac{1}{40} $ of the tank per minute.
- Tap B empties the tank in 60 minutes. Its emptying rate is $ \frac{1}{60} $ of the tank per minute.
Step 2: Calculate the Net Filling Rate
When both taps are open, the net filling rate is the difference between the filling rate and the emptying rate:
Net Rate = (Rate of Tap A) - (Rate of Tap B)
Net Rate = $ \frac{1}{40} \, \text{tank/min} - \frac{1}{60} \, \text{tank/min} $
To subtract these fractions, find a common denominator, which is 120:
Net Rate = $ \left( \frac{1 \times 3}{40 \times 3} \right) - \left( \frac{1 \times 2}{60 \times 2} \right) \, \text{tank/min} $
Net Rate = $ \frac{3}{120} - \frac{2}{120} \, \text{tank/min} $
Net Rate = $ \frac{1}{120} \, \text{tank/min} $
Step 3: Calculate the Total Time Taken
The time taken to fill the tank is the reciprocal of the net filling rate:
Time = $ \frac{1}{\text{Net Rate}} $
Time = $ \frac{1}{\frac{1}{120} \, \text{tank/min}} $
Time = $ 120 $ minutes
Conclusion
Therefore, the time taken to fill the tank when both taps are opened simultaneously is 120 minutes.
Similar Questions
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Important Questions from Pipe and Cistern
Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
There are two water taps in a tank which can fill the empty tank in 12 hours and 18 hours respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in 36 hours. If both the water taps are opened at the same time to fill the empty tank and leakage point was repaired after 1 hour, then in how much time the empty tank will be completely filled?
Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All the three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are opened together, but after 4 hours pipe B is closed. In how many hours, the empty tank will be completely filled?
Pipes A and B can fill a tank in 43.2 minutes and 108 minutes, respectively. Pipe C can empty it at 3 litres/minute. When all the three pipes are opened together, they fill the tank in 54 minutes. The capacity (in litres) of the tank is:
