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.