Joe checked his display in his car and saw that he traveled 97 km in 100 minutes. What is Joe’s average speed in miles per hour? The conversion factor you will need for this question is: 1 mile = 1.60934 km. (Round to the nearest tenth
The Correct Answer and Explanation is:
To find Joe’s average speed in miles per hour, we need to first convert the distance from kilometers to miles and the time from minutes to hours.
Step 1: Convert kilometers to miles
We are given that Joe traveled 97 kilometers, and we need to convert this into miles using the conversion factor:
1 mile = 1.60934 kilometers.
We can set up the conversion like this: Distance in miles=Distance in kilometersConversion factor\text{Distance in miles} = \frac{\text{Distance in kilometers}}{\text{Conversion factor}}Distance in miles=Conversion factorDistance in kilometers Distance in miles=971.60934≈60.3 miles\text{Distance in miles} = \frac{97}{1.60934} \approx 60.3 \, \text{miles}Distance in miles=1.6093497≈60.3miles
Step 2: Convert minutes to hours
Next, we need to convert the time from minutes to hours. We are told that Joe traveled for 100 minutes. There are 60 minutes in one hour, so we convert minutes to hours by dividing by 60: Time in hours=10060≈1.6667 hours\text{Time in hours} = \frac{100}{60} \approx 1.6667 \, \text{hours}Time in hours=60100≈1.6667hours
Step 3: Calculate the average speed
Now that we have the distance in miles (60.3 miles) and the time in hours (1.6667 hours), we can calculate the average speed by dividing the distance by the time: Average speed=Distance in milesTime in hours\text{Average speed} = \frac{\text{Distance in miles}}{\text{Time in hours}}Average speed=Time in hoursDistance in miles Average speed=60.31.6667≈36.2 miles per hour\text{Average speed} = \frac{60.3}{1.6667} \approx 36.2 \, \text{miles per hour}Average speed=1.666760.3≈36.2miles per hour
Final Answer:
Joe’s average speed is approximately 36.2 miles per hour.
In this calculation, the key steps involved converting both the distance from kilometers to miles and the time from minutes to hours, and then using the formula for average speed to get the final result.
