Bunuel wrote:
Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped out of the tank at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the tank increasing?
(1) The amount of water initially in the tank is 200 gallons.
(2) Water is pumped into the tank at a rate of 10 gallons per minute and out of the tank at a rate of 10 gallons every \(2\frac{1}{2}\) minutes.
We are given that water is flowing into a tank through an inlet pipe and out of the tank through an outlet pipe. We need to determine at what rate the amount of water in the tank is increasing.
Statement One Alone:The amount of water initially in the tank is 200 gallons.
Knowing the initial amount of water in the tank is not enough information to determine at what rate the amount of water in the tank is increasing. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:Water is pumped into the tank at a rate of 10 gallons per minute and out of the tank at a rate of 10 gallons every 2.5 minutes.
From statement two, we know the rate at which the water is flowing into the tank and also the rate at which the water is flowing out of the tank. With this information we can determine the “net rate,” or the rate at which the amount of water is increasing in the tank. The formula is: rate = work/time
rate in = 10/1 = 10 gallons per minute
rate out = 10/2.5 = 4 gallons per minute
Thus, the amount of water is increasing in the tank at a rate of 10 – 4 = 6 gallons per minute.
Statement two alone is sufficient to answer the question.
The answer is B.
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