Question

arun is driving on a long road trip. he wrote an equation to represent how many gallons of gas he has left in his tank, $g = 14 - 0.5h$, where $g$ represents the number of gallons and $h$ represents time in hours. what could the number 14 represent in the equation?

answer

• how long it takes arun to run out of gas.
• how quickly the car uses gas, in gallons per hour.
• the number of gallons of gas at time $h = 0$.
• the number of gallons in the tank when the trip ends.

Explanation:

Step1: Analyze the equation structure

The equation is \( g = 14 - 0.5h \), where \( g \) is gallons left and \( h \) is time in hours.

Step2: Evaluate each option

• "How long it takes Arun to run out of gas": This would be when \( g = 0 \), solving \( 0 = 14 - 0.5h \) gives \( h = 28 \), not 14. Eliminate.
• "How quickly the car uses gas": The rate is \( 0.5 \) gallons per hour (the coefficient of \( h \)), not 14. Eliminate.
• "The number of gallons of gas at time \( h = 0 \)": Substitute \( h = 0 \) into the equation: \( g = 14 - 0.5(0) = 14 \). This matches.
• "The number of gallons in the tank when the trip ends": The trip ends when gas is gone (\( g = 0 \)), not 14. Eliminate.

Answer:

The number of gallons of gas at time \( h = 0 \).