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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 fully 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 cons...
To solve this problem, we need to determine the rate at which water needs to be pumped into the tank in order to fill it in 10 minutes while simultaneously draining it at a constant rate.
Let's assume the rate of draining the tank is D gallons per minute and the rate of pumping water into the tank is P gallons per minute.
1. Determine the rate of draining the tank:
Since it takes 30 minutes to empty a half-full tank, the rate of draining the tank is given by the formula:
D = (0.5 tank volume) / 30 = (0.5V) / 30
2. Determine the rate of filling the tank:
In 10 minutes, the tank needs to be completely filled. Therefore, the rate of filling the tank is given by the formula:
P = V / 10
3. Equate the rates of draining and filling:
Since the tank is being drained and filled simultaneously, the rate of pumping water in should be equal to the rate of draining.
Therefore, we have the equation:
P = D
4. Substitute the values of P and D:
From step 2, we know that P = V / 10
From step 1, we know that D = (0.5V) / 30
Substituting these values into the equation from step 3, we get:
V / 10 = (0.5V) / 30
5. Solve for V:
To solve this equation, we can cross-multiply and simplify:
30V = 10 * 0.5V
30V = 5V
V = 0.1667
6. Determine the rate of pumping in water:
Now that we know the volume of the tank (V), we can determine the rate at which water needs to be pumped in to fill it in 10 minutes.
P = V / 10 = 0.1667 / 10 = 0.0167
7. Compare the rate of pumping to the rate of draining:
Since the rate of pumping water in is given by P, and the rate of draining is given by D, we can compare these rates:
P / D = 0.0167 / [(0.5 * 0.1667) / 30] = 0.0167 / 0.00833 = 2
Conclusion:
The rate at which water needs to be pumped into the tank so that it gets fully filled in 10 minutes is 2 times the draining rate. Therefore, the correct answer is option 'D'.
Let's assume the rate of draining the tank is D gallons per minute and the rate of pumping water into the tank is P gallons per minute.
1. Determine the rate of draining the tank:
Since it takes 30 minutes to empty a half-full tank, the rate of draining the tank is given by the formula:
D = (0.5 tank volume) / 30 = (0.5V) / 30
2. Determine the rate of filling the tank:
In 10 minutes, the tank needs to be completely filled. Therefore, the rate of filling the tank is given by the formula:
P = V / 10
3. Equate the rates of draining and filling:
Since the tank is being drained and filled simultaneously, the rate of pumping water in should be equal to the rate of draining.
Therefore, we have the equation:
P = D
4. Substitute the values of P and D:
From step 2, we know that P = V / 10
From step 1, we know that D = (0.5V) / 30
Substituting these values into the equation from step 3, we get:
V / 10 = (0.5V) / 30
5. Solve for V:
To solve this equation, we can cross-multiply and simplify:
30V = 10 * 0.5V
30V = 5V
V = 0.1667
6. Determine the rate of pumping in water:
Now that we know the volume of the tank (V), we can determine the rate at which water needs to be pumped in to fill it in 10 minutes.
P = V / 10 = 0.1667 / 10 = 0.0167
7. Compare the rate of pumping to the rate of draining:
Since the rate of pumping water in is given by P, and the rate of draining is given by D, we can compare these rates:
P / D = 0.0167 / [(0.5 * 0.1667) / 30] = 0.0167 / 0.00833 = 2
Conclusion:
The rate at which water needs to be pumped into the tank so that it gets fully filled in 10 minutes is 2 times the draining rate. Therefore, the correct answer is option 'D'.
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Community Answer
It takes 30 minutes to empty a half-full tank by draining it at a cons...
Lets say capacity of tank is 1 litre
draining rate = 0.5litre/30minutes = 1/60 litre/min
let filling rate = x litre/min
in 1 min tank gets x - (1/60) litre filled.
to fill the remaining half part we need 10mins
x - 1/60 litre → 1min
0.5 litre → 10 mins
0.5/(x - 1/60) = 10
solving, we get x = 4/60
which is 4 times more than draining rate.
draining rate = 0.5litre/30minutes = 1/60 litre/min
let filling rate = x litre/min
in 1 min tank gets x - (1/60) litre filled.
to fill the remaining half part we need 10mins
x - 1/60 litre → 1min
0.5 litre → 10 mins
0.5/(x - 1/60) = 10
solving, we get x = 4/60
which is 4 times more than draining rate.
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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 fully 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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