The track of a roller coaster is 1.265 miles long. The ride lasts for 2.3 minutes. What is the average speed of the roller coaster in miles per hour?
The Correct Answer and Explanation is:
To calculate the average speed of the roller coaster, we will first use the formula for average speed:
[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
]
Step 1: Understand the units of the problem
- The total distance traveled by the roller coaster is 1.265 miles.
- The total time of the ride is 2.3 minutes. However, we need to convert this time from minutes to hours since the desired answer is in miles per hour (mph).
Step 2: Convert time from minutes to hours
Since there are 60 minutes in one hour, to convert 2.3 minutes into hours, we divide by 60:
[
\text{Total Time in Hours} = \frac{2.3 \text{ minutes}}{60} = 0.03833 \text{ hours}
]
Step 3: Apply the formula for average speed
Now that we have the distance in miles (1.265 miles) and the time in hours (0.03833 hours), we can calculate the average speed:
[
\text{Average Speed} = \frac{1.265 \text{ miles}}{0.03833 \text{ hours}} = 33.03 \text{ mph}
]
Step 4: Conclusion
The average speed of the roller coaster is approximately 33.03 miles per hour.
Explanation
The problem asks for the average speed of the roller coaster over a specific distance and time. Since speed is defined as the distance traveled per unit of time, we apply the formula for average speed, ensuring that the units of time are converted from minutes to hours to match the unit of speed (miles per hour). After calculating the time in hours, we divide the total distance by the time in hours to obtain the average speed. Thus, the roller coaster travels at an average speed of about 33.03 mph during the ride.