Calculating Simultaneous Tank Emptying Time
This problem involves calculating the combined rate at which two taps empty a tank.
Understanding Tap Rates
- Tap A can empty the tank in 30 minutes. Its rate is \(\frac{1}{30}\) of the tank per minute.
- Tap B can empty the tank in 15 minutes. Its rate is \(\frac{1}{15}\) of the tank per minute.
Combined Emptying Rate
When both taps operate simultaneously, their rates add up.
- Combined Rate = Rate of Tap A + Rate of Tap B
- Combined Rate = \(\frac{1}{30} + \frac{1}{15}\)
- To add these fractions, find a common denominator, which is 30.
- Combined Rate = \(\frac{1}{30} + \frac{2}{30} = \frac{1+2}{30} = \frac{3}{30}\)
- Simplify the combined rate: \(\frac{3}{30} = \frac{1}{10}\) of the tank per minute.
Total Time Calculation
The time needed to empty the tank is the reciprocal of the combined rate.
- Time = \(\frac{1}{\text{Combined Rate}}\)
- Time = \(\frac{1}{\frac{1}{10}}\)
- Time = \(10\) minutes.
Therefore, if both taps operate simultaneously, it will take 10 minutes to empty the tank.
Similar Questions
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Minute 1: Only A
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