A car traveled 36 miles in 45 minutes. The car traveled at a constant speed. If the car continues to travels at this rate which equation can be used to determine y the total number of miles the car will travel in x hours
The Correct Answer and Explanation is:
To solve this problem, we need to first understand the relationship between the time and the distance traveled by the car. Since the car is traveling at a constant speed, the number of miles traveled varies directly with the time.
Step 1: Find the speed of the car
The car travels 36 miles in 45 minutes. We need to convert the time to hours to make it compatible with the equation, since the problem asks for the total miles traveled in terms of hours.
- 45 minutes = 45/60 hours = 0.75 hours
Now we can find the car’s speed (in miles per hour): Speed=DistanceTime=36 miles0.75 hours=48 miles per hour\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{36 \text{ miles}}{0.75 \text{ hours}} = 48 \text{ miles per hour}Speed=TimeDistance=0.75 hours36 miles=48 miles per hour
Step 2: Set up the equation
The speed of the car is 48 miles per hour. This means for every hour, the car will travel 48 miles. Now, we can express the total distance traveled, yyy, as a function of time, xxx, in hours.
The equation to determine the total number of miles the car will travel in xxx hours is: y=48xy = 48xy=48x
Where:
- yyy is the total number of miles,
- xxx is the number of hours.
Explanation:
The relationship between the number of hours xxx and the total distance yyy is linear because the car is traveling at a constant speed. The slope of the line is the speed of the car, which is 48 miles per hour. This means for each additional hour, the car will travel 48 more miles.
