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.
(1) The amount of water initially in the tank is 200 gallons. Clearly insufficient.
(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. Since water is pumped out of the tank at a rate of 10 gallons every \(2\frac{1}{2}=\frac{5}{2}\) minutes, then it's pumped out at a rate of \(\frac{10}{(\frac{5}{2})}=4\) gallons per minute, hence the net increase is \(10-4=6\) gallons per minute. Sufficient.
Answer: B.