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Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously?
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Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap...
Understanding the Problem
To find out how long it takes to fill the reservoir when all three taps are opened simultaneously, we first need to identify their rates of work.
Rates of the Taps
- Tap 1 fills the tank in 6 hours:
- Rate = 1/6 tank per hour.
- Tap 2 fills the tank in 8 hours:
- Rate = 1/8 tank per hour.
- Tap 3 empties the tank in 15 hours:
- Rate = -1/15 tank per hour (negative because it is emptying).
Combined Rate Calculation
Now, we combine the rates of all three taps:
- Combined Rate = Rate of Tap 1 + Rate of Tap 2 + Rate of Tap 3
- Combined Rate = (1/6) + (1/8) - (1/15)
To add these fractions, we find a common denominator, which is 120.
- (1/6) = 20/120
- (1/8) = 15/120
- (1/15) = 8/120
Now, substituting back:
- Combined Rate = (20/120) + (15/120) - (8/120) = (27/120)
Final Calculation
- The combined rate simplifies to (9/40) tank per hour.
To find the time to fill one tank:
- Time = 1 / (Combined Rate)
- Time = 1 / (9/40) = 40/9 hours.
Conclusion
Thus, it would take approximately 4.44 hours, or 4 hours and 26 minutes, to fill the water reservoir when all three taps are opened simultaneously.
To find out how long it takes to fill the reservoir when all three taps are opened simultaneously, we first need to identify their rates of work.
Rates of the Taps
- Tap 1 fills the tank in 6 hours:
- Rate = 1/6 tank per hour.
- Tap 2 fills the tank in 8 hours:
- Rate = 1/8 tank per hour.
- Tap 3 empties the tank in 15 hours:
- Rate = -1/15 tank per hour (negative because it is emptying).
Combined Rate Calculation
Now, we combine the rates of all three taps:
- Combined Rate = Rate of Tap 1 + Rate of Tap 2 + Rate of Tap 3
- Combined Rate = (1/6) + (1/8) - (1/15)
To add these fractions, we find a common denominator, which is 120.
- (1/6) = 20/120
- (1/8) = 15/120
- (1/15) = 8/120
Now, substituting back:
- Combined Rate = (20/120) + (15/120) - (8/120) = (27/120)
Final Calculation
- The combined rate simplifies to (9/40) tank per hour.
To find the time to fill one tank:
- Time = 1 / (Combined Rate)
- Time = 1 / (9/40) = 40/9 hours.
Conclusion
Thus, it would take approximately 4.44 hours, or 4 hours and 26 minutes, to fill the water reservoir when all three taps are opened simultaneously.
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Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously?
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Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously? 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 fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously?.
Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously? 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 fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two taps fill a water reservoir in 6 and 8 hours respectively. 3rd tap can empty the completely filled water reservoir in 15 hours. How long would it take to fill the empty tank, if all of them are opened simultaneously?.
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