Question

A tank that currently contains 2500 gallons of oil is being emptied at a rate of 25 gallons per minute. The capacity of this tank is 3000 gallons. Let c be the capacity of the tank, and t be the time. Write an equation that relates the two quantities.​

Answer 1

To relate the tank's capacity with time, we use the equation c = 2500 - 25t, where c is the capacity of the tank in gallons and t is the time in minutes.

Step-by-step explanation:

To relate the capacity of the tank (c) with the time (t), we can use the information given about the rate at which the tank is being emptied. We know that 25 gallons of oil are being emptied each minute. Since the tank originally contains 2500 gallons, we can write an equation that decreases the amount of oil in the tank over time.

The equation is: c = 2500 - 25t

Here, c is the capacity of the tank in gallons at any given time t, where t is the time in minutes. When t is 0 (at the beginning), c is 2500 gallons (the initial amount of oil in the tank).

Answer 2

The rate at which the tank is being emptied is 25 gallons per minute, which means that the change in the amount of oil in the tank per minute is -25. Let's assume that the initial amount of oil in the tank is 2500 gallons and the capacity of the tank is 3000 gallons.

The equation that relates the amount of oil in the tank, V, and time, t, is given by:

V = 2500 - 25t

This equation represents a linear relationship between the amount of oil in the tank and time. As time increases, the amount of oil in the tank decreases linearly at a rate of 25 gallons per minute.

The capacity of the tank, c, is 3000 gallons, which means that the tank will be completely emptied after:

t = (3000 - 2500) / 25 = 20 minutes

After 20 minutes, the amount of oil in the tank will be:

V = 2500 - 25(20) = 2000 gallons