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?
Show workings
Weight when half full = 310kg
Weight when three quarters full = 450kg
Weight of water when half full = 310kg
Weight of water when three quarters full = 450kg - 310kg = 140kg
Weight of tank when empty = 310kg - 140kg = 170kg
To find the weight of the tank when it is empty, we need to find the weight of the water in the tank when it is half full and when it is three-quarters full.
Let's denote the weight of the empty tank as "T" and the weight of water as "W."
According to the given information, the tank weighs 310kg when it is half full of water, so we can set up the equation:
T + W/2 = 310 (equation 1)
Similarly, the tank weighs 450kg when it is three-quarters full of water:
T + W*(3/4) = 450 (equation 2)
To solve these equations simultaneously, we can use the method of substitution.
Starting with equation 1, we can isolate T:
T = 310 - W/2 (equation 3)
Now substitute equation 3 into equation 2:
(310 - W/2) + W*(3/4) = 450
Multiplying through by 4 to eliminate the fractions:
(4*310 - 2W) + 3W = 4*450
(1240 - 2W) + 3W = 1800
1240 + W = 1800
Simplifying:
W = 1800 - 1240
W = 560
Now substitute the value of W back into equation 3 to find T:
T = 310 - 560/2
T = 310 - 280
T = 30
Therefore, the weight of the tank when it is empty is 30kg.
Let's call the weight of the empty tank "W" kg.
Given:
Weight of tank + half-full water = 310 kg
Weight of tank + three quarters full water = 450 kg
First, we need to find the weight of the water in the tank when it is half full and three quarters full.
Weight of half-full water = 310 kg - W kg ---(Equation 1)
Weight of three quarters full water = 450 kg - W kg ---(Equation 2)
Now, we can set up a proportion to solve for the weight of the water when the tank is half full and three quarters full.
(half full water weight) / (three quarters full water weight) = (half full tank weight) / (three quarters full tank weight)
Substituting the given values:
(310 kg - W kg) / (450 kg - W kg) = (W kg + (310 kg - W kg)) / (W kg + (450 kg - W kg))
Simplifying the equation:
(310 - W) / (450 - W) = (310 + W) / 450
Cross multiplying:
(310 - W)(450) = (310 + W)(450 - W)
Expanding the equation:
139500 - 450W = 139500 + 310W - W^2
Rearranging the equation:
W^2 - 760W = 0
Now we can solve for W by factoring:
W(W - 760) = 0
Setting each factor equal to zero:
W = 0 or W - 760 = 0
Since the weight of the tank cannot be zero, we can disregard the solution W = 0.
Therefore, the weight of the empty tank (W) is 760 kg.