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It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets hilly filled in 10 minutes?
- a)4 times the draining rate
- b)3 times the draining rate
- c)2.5 times the draining rate
- d)2 times the draining rate
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
It takes 30 minutes to empty a half-full tank by draining it at a con...
Given in the question that; Vhalf = 30(s)
Let us take drawing rate = s
Total volume = 60 S tank
(s1)(10) – (s)10 = 30s
s1(s) – s = 3s
s1 = 4s
s1 = 4 times the drawing rate.
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It takes 30 minutes to empty a half-full tank by draining it at a con...
Problem Analysis:
Let's assume that the draining rate is D liters/minute and the rate at which water is pumped in is P liters/minute.
Given:
- It takes 30 minutes to empty a half-full tank by draining it at a constant rate.
- It is decided to simultaneously pump water into the half-full tank while draining it.
- The tank needs to be fully filled in 10 minutes.
Approach:
To solve this problem, we can use the concept of work.
Work Done by Draining:
- The work done by draining is equal to the product of the draining rate and the time taken to drain the tank.
- Work done by draining = D * 30 (since it takes 30 minutes to empty the half-full tank)
Work Done by Pumping:
- The work done by pumping is equal to the product of the pumping rate and the time taken to fill the tank.
- Work done by pumping = P * 10 (since it takes 10 minutes to fill the tank)
Total Work:
- The total work done is the sum of the work done by draining and the work done by pumping.
- Total work = D * 30 + P * 10
Since the tank is half-full at the beginning, the total work done should be equal to filling a full tank.
Equation:
D * 30 + P * 10 = 1 (since the total work done should be equal to filling a full tank)
Solving for P:
Let's solve the equation for P to find the rate at which water has to be pumped in.
D * 30 + P * 10 = 1
P * 10 = 1 - D * 30
P = (1 - D * 30) / 10
Simplification:
P = (1 - 3D) / 10
Comparing Options:
We need to find the rate at which water has to be pumped in, which is represented by P.
Comparing the equation P = (1 - 3D) / 10 with the given options:
a) P = 4D, which is not equivalent to (1 - 3D) / 10
b) P = 3D, which is not equivalent to (1 - 3D) / 10
c) P = 2.5D, which is not equivalent to (1 - 3D) / 10
d) P = 2D, which is not equivalent to (1 - 3D) / 10
None of the options match the equation (1 - 3D) / 10, so none of the given options are correct.
Therefore, the correct answer cannot be determined from the given options.
Let's assume that the draining rate is D liters/minute and the rate at which water is pumped in is P liters/minute.
Given:
- It takes 30 minutes to empty a half-full tank by draining it at a constant rate.
- It is decided to simultaneously pump water into the half-full tank while draining it.
- The tank needs to be fully filled in 10 minutes.
Approach:
To solve this problem, we can use the concept of work.
Work Done by Draining:
- The work done by draining is equal to the product of the draining rate and the time taken to drain the tank.
- Work done by draining = D * 30 (since it takes 30 minutes to empty the half-full tank)
Work Done by Pumping:
- The work done by pumping is equal to the product of the pumping rate and the time taken to fill the tank.
- Work done by pumping = P * 10 (since it takes 10 minutes to fill the tank)
Total Work:
- The total work done is the sum of the work done by draining and the work done by pumping.
- Total work = D * 30 + P * 10
Since the tank is half-full at the beginning, the total work done should be equal to filling a full tank.
Equation:
D * 30 + P * 10 = 1 (since the total work done should be equal to filling a full tank)
Solving for P:
Let's solve the equation for P to find the rate at which water has to be pumped in.
D * 30 + P * 10 = 1
P * 10 = 1 - D * 30
P = (1 - D * 30) / 10
Simplification:
P = (1 - 3D) / 10
Comparing Options:
We need to find the rate at which water has to be pumped in, which is represented by P.
Comparing the equation P = (1 - 3D) / 10 with the given options:
a) P = 4D, which is not equivalent to (1 - 3D) / 10
b) P = 3D, which is not equivalent to (1 - 3D) / 10
c) P = 2.5D, which is not equivalent to (1 - 3D) / 10
d) P = 2D, which is not equivalent to (1 - 3D) / 10
None of the options match the equation (1 - 3D) / 10, so none of the given options are correct.
Therefore, the correct answer cannot be determined from the given options.
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It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets hilly filled in 10 minutes?a)4 times the draining rateb)3 times the draining ratec)2.5 times the draining rated)2 times the draining rateCorrect answer is option 'A'. Can you explain this answer?
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