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Two pipes can fill a tank in 25 and 30 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
- a)250 gallons
- b)450 gallons
- c)120 gallons
- d)150 gallons
Correct answer is option 'B'. Can you explain this answer?
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Two pipes can fill a tank in 25 and 30 minutes respectively and a wast...
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Solution:
Let the capacity of the tank be x gallons.
The given time taken by the first pipe to fill the tank is 25 minutes. Hence, the rate of filling of the first pipe is:
1/25 tank/minute
Similarly, the rate of filling of the second pipe is:
1/30 tank/minute
The waste pipe empties 3 gallons per minute. Hence, the rate of emptying of the waste pipe is:
3 gallons/minute
Let the rate of filling of all the three pipes working together be y tank/minute.
According to the question, all the three pipes working together can fill the tank in 15 minutes. Hence, we can write:
y * 15 = x
Simplifying the above equation, we get:
y = x/15
Now, we can write the following equation based on the rates of filling and emptying:
1/25 + 1/30 - 3/x = y
Substituting the value of y, we get:
1/25 + 1/30 - 3/x = x/15
Simplifying the above equation, we get:
x = 450
Therefore, the capacity of the tank is 450 gallons.
Answer: Option B (450 gallons)
Let the capacity of the tank be x gallons.
The given time taken by the first pipe to fill the tank is 25 minutes. Hence, the rate of filling of the first pipe is:
1/25 tank/minute
Similarly, the rate of filling of the second pipe is:
1/30 tank/minute
The waste pipe empties 3 gallons per minute. Hence, the rate of emptying of the waste pipe is:
3 gallons/minute
Let the rate of filling of all the three pipes working together be y tank/minute.
According to the question, all the three pipes working together can fill the tank in 15 minutes. Hence, we can write:
y * 15 = x
Simplifying the above equation, we get:
y = x/15
Now, we can write the following equation based on the rates of filling and emptying:
1/25 + 1/30 - 3/x = y
Substituting the value of y, we get:
1/25 + 1/30 - 3/x = x/15
Simplifying the above equation, we get:
x = 450
Therefore, the capacity of the tank is 450 gallons.
Answer: Option B (450 gallons)
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Two pipes can fill a tank in 25 and 30 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)250 gallonsb)450 gallonsc)120 gallonsd)150 gallonsCorrect answer is option 'B'. Can you explain this answer?
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