Question

Suppose you start with a full tank of gas (14 gallons) in your truck. After driving 5 hours, you now have 5 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing? State your answer as a reduced fraction.

Answer 1

We can use the formula for average rate of change to find the rate at which the gas is being used:

average rate of change = (change in y) / (change in x)

where y is the number of gallons left in the tank and x is the number of hours driven.

Substituting the given values, we get:

average rate of change = (5 - 14) / (5 - 0)

Simplifying, we get:

average rate of change = -9/5

Therefore, the rate at which the gas is being used is -9/5 gallons per hour, or -1.8 gallons per hour. This means that the gas in the tank is decreasing at a rate of 1.8 gallons per hour.