A water tank is being filled with water. The volume of water in the water tank varies with time. The tank contains 200 liters of water after 2 minutes.

Define appropriate variables, and write an equation relating the volume of water and time. What does the constant variation represent?
Please help I don't know where to start.

This appears to be a problem involving direct variation. So, you know that the equation will look like

v = kt

k represents the rate of fill, in liters/min. Since v(2) = 200,

200 = 2k, so k=100

Thus, the final equation must be

v = 100t

To define appropriate variables and write an equation relating the volume of water and time, we can use the following:

- Let V represent the volume of water in the tank (in liters)
- Let t represent the time passed (in minutes)

Based on the given information, we know that after 2 minutes, the tank contains 200 liters of water. This means that when t = 2, V = 200.

To find the equation that relates the volume of water and time, we need to determine the relationship between V and t. In this case, we can assume that the volume of water is increasing linearly with time, assuming a constant rate.

We can represent this relationship with a linear equation in the form of y = mx + b, where y represents the volume of water and x represents the time. The constant variation, represented by m, is the rate at which the volume of water is changing with respect to time.

In this scenario, as time increases, the volume of water in the tank is increasing at a constant rate. Therefore, we can write the equation as:

V = mt + b

To find the values of m and b, we can use the given information that when t = 2, V = 200. Plugging these values into the equation, we have:

200 = m(2) + b

Since b is the initial volume of water in the tank, we know that when t = 0, V = b. In this case, we are not given the initial volume, so we can't determine the exact value of b. However, we can say that when t = 0, V = b, and we can rewrite the equation as:

V = mt + b

In this equation, the constant variation, represented by m, represents the rate at which the volume of water is increasing with respect to time.