Superman is able to travel from Metropolis to Gotham City in 6.8 minutes, flying at a leisurely pace. If he flew at a speed of 344 meters per second, how far apart are the cities, in miles?
The Correct Answer and Explanation is:
To determine how far apart Metropolis and Gotham City are, we can use the formula for distance:
[
\text{Distance} = \text{Speed} \times \text{Time}
]
Given:
- Superman’s speed = 344 meters per second (m/s)
- Time = 6.8 minutes
Step 1: Convert time from minutes to seconds
Since the speed is given in meters per second, we need to convert the time from minutes to seconds. There are 60 seconds in a minute, so:
[
6.8 \, \text{minutes} = 6.8 \times 60 = 408 \, \text{seconds}
]
Step 2: Calculate the distance in meters
Now that we have the time in seconds, we can calculate the distance Superman travels:
[
\text{Distance} = 344 \, \text{m/s} \times 408 \, \text{seconds} = 140,352 \, \text{meters}
]
Step 3: Convert meters to miles
To convert the distance from meters to miles, we use the conversion factor:
[
1 \, \text{mile} = 1,609.34 \, \text{meters}
]
Thus, the distance in miles is:
[
\text{Distance in miles} = \frac{140,352 \, \text{meters}}{1,609.34 \, \text{meters/mile}} \approx 87.1 \, \text{miles}
]
Final Answer:
The distance between Metropolis and Gotham City is approximately 87.1 miles.
Explanation:
We started with Superman’s speed of 344 meters per second and the time he traveled, which was 6.8 minutes. After converting the time into seconds (408 seconds), we used the basic distance formula to find the distance in meters. Finally, we converted that distance from meters to miles using the conversion factor between meters and miles. The result is the distance between the two cities, which is approximately 87.1 miles.