An agricultural drone is spraying liquid fertilizer on a field at a constant rate. The tot… — SAT

An agricultural drone is spraying liquid fertilizer on a field at a constant rate. The total amount of fertilizer remaining in the drone's tank, in liters, can be modeled by a linear function of the time, in minutes, since the drone began spraying. After $3$ minutes of spraying, $84$ liters of fertilizer remain in the tank. After $8$ minutes of spraying, $54$ liters of fertilizer remain in the tank. How many minutes of spraying will it take for the tank to become completely empty?

Answer: 17 minutes

Answer

The correct answer is 17. The volume of fertilizer in the tank decreases at a constant rate of 6 liters per minute. Since 84 liters remain after 3 minutes, the initial volume of fertilizer in the tank was 102 liters. Dividing the initial volume of 102 liters by the rate of 6 liters per minute yields 17 minutes for the tank to be completely empty.

Step-by-Step Solution

Calculate the constant rate of change (slope) of the remaining fertilizer volume.

-6 liters per minute

The slope formula is used with the two data points representing time and volume:

(3, 84)

and

(8, 54)

Determine the initial volume of fertilizer in the tank (y-intercept).

102 liters

Using the slope-intercept form

F(t) = mt + b

, we substitute the slope

m = -6

and the point

(3, 84)

to solve for

b

Find the time when the volume of remaining fertilizer reaches 0.

17 minutes

Setting the linear function equal to 0 and solving for time gives the total duration until the tank is empty.

Key Concept

Linear Functions and Graphs

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