Calculating Combined Filling Time
This problem involves calculating the time taken for two taps working together to fill a pool, based on their individual filling times.
Tap A's Filling Rate
Tap A fills the pool in 10 hours. Its rate of filling is:
Rate_A = \(\frac{1 \text{ pool}}{10 \text{ hours}} = \frac{1}{10}\) pool/hour
Tap B's Filling Rate
Tap B fills the pool in 15 hours. Its rate of filling is:
Rate_B = \(\frac{1 \text{ pool}}{15 \text{ hours}} = \frac{1}{15}\) pool/hour
Combined Filling Rate
When both taps work together, their rates add up. The combined rate is:
Combined Rate = Rate_A + Rate_B
Combined Rate = \(\frac{1}{10} + \frac{1}{15}\)
To add these fractions, we find a common denominator, which is 30:
Combined Rate = \(\frac{3}{30} + \frac{2}{30} = \frac{5}{30}\)
Simplifying the fraction:
Combined Rate = \(\frac{1}{6}\) pool/hour
Total Time Taken Together
The time taken to fill the pool together is the reciprocal of the combined rate:
Time = \(\frac{1}{\text{Combined Rate}}\)
Time = \(\frac{1}{1/6 \text{ pool/hour}}\)
Time = 6 hours
Therefore, the two taps will take 6 hours to fill the empty pool together.
Similar Questions
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