A rectangular tank weighs 310kg,when it is half full of water and 450kg ,when it is three quarter full of water.What is the weight of the empty tank?
weight of water when full --- x kg
weight of empty tank ------- y kg
(1/2)x + y = 310 **
(3/4)x + y = 450 ***
subtract: *** - **
(1/4)x = 140
x = 560
back in **
280 + y =310
y = 30
the tank weighs 30 kg
How did the 280 come about?
Substitute 560 into equation** I.e (1/2) × 560=280
140×4=560
The 560 and the 280 i dont really know how they come about
Well, this rectangular tank is going through some serious weight issues! It gets all bloated when it's full of water! Let's try to break down the problem, shall we?
When the tank is half full, it weighs 310kg. And when it's three-quarters full, it weighs 450kg. So, the difference in weight between these two levels is 450kg - 310kg, which gives us a weight of 140kg for that additional quarter.
Since each quarter of the tank has a weight of 140kg, we can conclude that the total weight of the tank when it's completely full is 450kg + 140kg = 590kg.
But hold on a second, we still need to find out the weight of the empty tank. So, if the tank weighs 590kg when it's full, and we subtract the weight of the water (which is 450kg), we can deduce that the weight of the empty tank is 590kg - 450kg = 140kg.
Phew, that was quite the math workout! So, the weight of the empty tank is a puny 140kg.
To solve this problem, we can use the concept of buoyancy.
Let's say the weight of the empty tank is W kg.
When the tank is half full of water, the weight of the tank plus the weight of the water will be 310 kg. This can be represented as:
W + (0.5 * W) = 310 kg
Simplifying this equation, we find:
1.5 * W = 310 kg
Dividing both sides of the equation by 1.5, we get:
W = 310 kg / 1.5
W ≈ 206.67 kg
So, the weight of the empty tank is approximately 206.67 kg.