A rectangular tank weighs 310kg, when it is half full of water and 450kg, when it is three quarters full of water. What is the weight of the tank when it is empty ?

Let the weight of the empty tank be x kg.

When the tank is half full of water, the weight of the water is 310 - x kg.

When the tank is three quarters full of water, the weight of the water is 450 - x kg.

Since the weight of water is directly proportional to the volume of water, we can set up the following proportion:

(310 - x) / x = (450 - x) / (x + (450 - x))

Solving this equation, we get:

(310 - x) / x = (450 - x) / 450

Cross multiplying, we get:

(310 - x) * 450 = x * (450 - x)

139500 - 450x = 450x - x^2

Rearranging, we get:

x^2 - 900x + 139500 = 0

Solving this quadratic equation, we get:

x = 150 or x = 930

Since the weight of the tank cannot be negative, the weight of the empty tank is 150 kg.

Let the weight of the tank be X kg.
Weight of water when the tank is half full = (1/2) - (Volume of the tank) - (Density of water)
= (1/2) - X - 1000 = 500X kg
Weight of water when the tank is three quarters full = (3/4) - X - 1000 = 750X kg

Given that,
Weight of the tank when it is half full of water = 310 kg
Therefore,
310 = X + 500X
510X = 310
X = 310/510
X = 0.607 kg

Therefore, the weight of the tank when it is empty is 0.607 kg.