A car travels at a constant speed. It consumes 0.035 gallons of gas for each mile traveled on a horizontal road and 0.04 gallons per mile traveled on an inclined road. Which of the following expressions represents the amount, in gallons, that the car consumes if it travels ℎ miles on the horizontal road and 𝑐 miles on the inclined road?
We’re interested in the amount in gallons a car uses for traveling on two different types of roads. A horizontal road and an inclined road. The rate of gallons consumed per mile on the horizontal road is 0.035. And the rate of gallons per mile on the inclined road is 0.04. To find the total amount consumed, we’ll take the gallons used on the horizontal road. And we’ll add the gallons used on the inclined road. Any of the expressions that use subtraction will not be helpful for us. We need to add the gallons used on either type of road. And so we can exclude both option C and option D.
To find the gallons used on the horizontal road, you’ll need to know how many gallons per mile you use. And then multiply that by the number of miles you go. The number of miles driven on the horizontal road is ℎ. That’s the variable we need to use. And the number of gallons per mile on the horizontal road is 0.035. We multiply 0.035 by ℎ to get the gallons used on the horizontal road. And we’ll be adding the gallons per mile of the inclined road multiplied by the number of miles driven on the inclined road.
For the inclined road, we need to use the variable 𝑐 for the number of miles. And the number of gallons per mile on the inclined road is 0.04. The gallons used on the inclined road is 0.04𝑐. And so our expression is 0.035ℎ plus 0.04𝑐. Option A. If we look closely at option B, we see that they have switched the gallons per mile. They’ve used the gallons per mile on the inclined road and multiplied that by the number of miles driven on the horizontal road. And this won’t work.
The only expression that could be used to calculate how much gas the car consumes when it’s traveling on these two types of roads would be option A, 0.035ℎ plus 0.04𝑐.