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Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely?
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Two taps a and b fill an overhead water tank in 12 hours and eight hou...
Understanding the Problem
To determine how long it takes for taps A and B to fill the tank together, we first need to find their individual rates of filling.
Individual Rates of Filling
- Tap A fills the tank in 12 hours.
- Rate of A = 1 tank/12 hours = 1/12 tanks per hour.
- Tap B fills the tank in 8 hours.
- Rate of B = 1 tank/8 hours = 1/8 tanks per hour.
Combined Rate of Filling
Next, we add the rates of both taps to find their combined rate:
- Combined Rate = Rate of A + Rate of B
- Combined Rate = 1/12 + 1/8
Finding a Common Denominator
To add these fractions, we need a common denominator. The least common multiple of 12 and 8 is 24.
- Rate of A = 2/24 tanks per hour (1/12 converted)
- Rate of B = 3/24 tanks per hour (1/8 converted)
Calculating Combined Rate
Now we can add the rates:
- Combined Rate = 2/24 + 3/24 = 5/24 tanks per hour.
Time to Fill the Tank
To find the time taken to fill one tank, we take the reciprocal of the combined rate:
- Time = 1 / (5/24) = 24/5 hours = 4.8 hours.
Conclusion
Therefore, when both taps A and B are opened together, they will take 4.8 hours to fill the tank completely.
To determine how long it takes for taps A and B to fill the tank together, we first need to find their individual rates of filling.
Individual Rates of Filling
- Tap A fills the tank in 12 hours.
- Rate of A = 1 tank/12 hours = 1/12 tanks per hour.
- Tap B fills the tank in 8 hours.
- Rate of B = 1 tank/8 hours = 1/8 tanks per hour.
Combined Rate of Filling
Next, we add the rates of both taps to find their combined rate:
- Combined Rate = Rate of A + Rate of B
- Combined Rate = 1/12 + 1/8
Finding a Common Denominator
To add these fractions, we need a common denominator. The least common multiple of 12 and 8 is 24.
- Rate of A = 2/24 tanks per hour (1/12 converted)
- Rate of B = 3/24 tanks per hour (1/8 converted)
Calculating Combined Rate
Now we can add the rates:
- Combined Rate = 2/24 + 3/24 = 5/24 tanks per hour.
Time to Fill the Tank
To find the time taken to fill one tank, we take the reciprocal of the combined rate:
- Time = 1 / (5/24) = 24/5 hours = 4.8 hours.
Conclusion
Therefore, when both taps A and B are opened together, they will take 4.8 hours to fill the tank completely.
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Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely?
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Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely?.
Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two taps a and b fill an overhead water tank in 12 hours and eight hours respectively if both of them are opened together how long would they take to fill the tank completely?.
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