# Maths question – water poured into two tanks

Maths tip:

"Water was poured into an empty rectangular Tank J (Length 40cm,width 20cm ) until it reached a height of 25cm. There was 2.2 litres of water in Tank M (Length 20cm, width 20cm) . Water was then poured from Tank J to Tank M until the heights of the water in both tanks were the same. What was the volume of water in Tank J in the end? Is there another method besides guess and check?"

Method 1 (Algebra)
Let height of water in both tanks be x (they are the same in both)
Volume of water in J initially = 25*40*20=20 litres.
Volume of water in M initially = 2.2 litres.
Total volume = 22.2 litres.
sum of water in both tanks in the end = 22.2litres.
40*20*x + 20*20*x = 22.2 * 1000
2x+x = 55.5
3x = 55.5
x = 18.5
volume of water in tank J in the end = 18.5*40*20=14800ml = 14.8litres.

Method 2 (Model)
Volume of water in J initially = 25*40*20=20 litres.
Volume of water in M initially = 2.2 litres.
Total volume = 22.2 litres.
Base area of J is 2 times of M.
For the same height, volume of J is 2 times of M.
J: [][]
M: []
Total: [][][] = 22.2 litres.
so volume of J = [][] = 14.8 litres.

Method 3 (Supposition / Speed)
Height of water in M initially = 2.2*1000/20/20 = 5.5cm
Suppose 1cm of water in J was poured into M. J would have reduced from 25cm to 24cm, while M increased from 5.5cm to 7.5cm.
So for every 1cm decrease in J, 2cm increase in M.
It becomes a speed question, where J is moving down at 1cm at a time, while M is moving up 2cm at a time (total speed = 3cm). They are 25-5.5 = 19.5cm apart. J will need to move down 19.5/3 = 6.5cm while M will need to move 19.5/3*2 = 13cm.
Final height of J = 25-6.5 = 18.5cm
Volume of J = 18.5*40*20/1000 = 14.8litres