alex.gellatly wrote:Reserve tank 1 is capable of holding z gallons of water. Water is pumped into tank 1, which starts off empty, at a rate of x gallons per minute. Tank 1 simultaneously leaks water at a rate of y gallons per minute (where x > y). The water that leaks out of tank 1 drips into tank 2, which also starts out empty. If the total capacity of tank 2 is twice the number of gallons of water actually existing in tank 1 after one minute, does tank 1 fill up before tank 2?

(1) zy < 2x^2 - 4xy + 2y^2
(2) The total capacity of tank 2 is less than one-half that of tank 1.

• ## z/(x - y) < 2(x - y)/y
  --> yz < 2(x - y)²

• x = 4, y = 2, z = 10 ---> Time to feel T1 = 10/(4 - 2) = 5 > Time to feel T2 = 2(4 - 2)/2 = 2
  x = 4, y = 1, z = 15 ---> Time to feel T1 = 15/(4 - 1) = 5 < Time to feel T2 = 2(4 - 1)/1 = 6