# Find water left in a tank using arithmetic sequences

by Problem posted Whitney Hamilton

(Edmond, OK, United States)

A water tank is emptied at a constant rate. Initially, 36,000 gallons of water were in the tank. A the end of five hours, 16,000 gallons remained. How many gallons of water were in the tank at the end of the third hour?

**Solution**

In order to get to 16000 gallons, we have to subtract a number. Since this number is constant, it is the same number we subtract each time.

Let us call this number we subtract n.

First hour: 36000

Second hour: 36000 - n

Third hour: 36000 - n - n

Fourth hour: 36000 - n - n - n

Fifth hour: 36000 - n - n - n - n

At this point, what is left in the tank is

36000 - n - n - n - n

It is also equal to 16000 as stated in the problem.

Therefore,

36000 - n - n - n - n = 16000

36000 - 4n = 16000

36000 - 16000 = 4n

20000 = 4n

20000/4 = 4n/4

5000 = n

Therefore, the number to subtract each time is 5000

Third hour: 36000 - 5000 - 5000 = 26000

There are 26000 gallons of water in the tank at the end of the third hour.