Imagine a full 1,500 liter water tank that springs a leak, losing 2 liters per minute. We could represent the number of liters left in the tank with the expression , where represents the number of minutes the tank has been leaking.

Now imagine at the same time, a second tank has 300 liters and is being filled at a rate of 6 liters per minute. We could represent the amount of water in liters in this second tank with the expression , where represents the number of minutes that have passed.

Since one tank is losing water and the other is gaining water, at some point they will have the same amount of water—but when? Asking when the two tanks have the same number of liters is the same as asking when (the number of liters in the first tank after minutes) is equal to (the number of liters in the second tank after minutes),

Solving for gives us minutes. So after 150 minutes, the number of liters of the first tank is equal to the number of liters of the second tank. We can check our answer and find the number of liters in each tank by substituting 150 for in the original expressions.

Using the expression for the first tank, we get which is equal to , or 1,200 liters.

If we use the expression for the second tank, we get , or just , which is also 1,200 liters. That means that after 150 minutes, each tank has 1,200 liters.