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Answer :
To find Tony Kanaan's average speed in the Indianapolis 500, we need to calculate the total time he took to complete the race and then use this to find his speed in miles per hour.
Step 1: Convert the race time into hours.
Tony's race time was 2 hours, 40 minutes, and 3.4181 seconds. We need to convert all of this time into hours:
- Hours: Already given as 2 hours.
- Minutes: 40 minutes need to be converted into hours. Since there are 60 minutes in an hour, we divide by 60:
[tex]\[ \frac{40}{60} \approx 0.6667 \, \text{hours} \][/tex]
- Seconds: 3.4181 seconds need to be converted into hours. Since there are 3600 seconds in an hour, we divide by 3600:
[tex]\[ \frac{3.4181}{3600} \approx 0.000949 \, \text{hours} \][/tex]
Now, add these values together to find the total time in hours:
[tex]\[ 2 + 0.6667 + 0.000949 \approx 2.6676 \, \text{hours} \][/tex]
Step 2: Calculate the average speed.
The distance of the race is 500 miles. To find the average speed, use the formula:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time in hours}} \][/tex]
[tex]\[ \text{Average speed} = \frac{500 \, \text{miles}}{2.6676 \, \text{hours}} \approx 187.433 \, \text{miles per hour} \][/tex]
Therefore, Tony Kanaan's average speed in the race was approximately 187.433 miles per hour when rounded to the thousandth of a mile per hour.
Step 1: Convert the race time into hours.
Tony's race time was 2 hours, 40 minutes, and 3.4181 seconds. We need to convert all of this time into hours:
- Hours: Already given as 2 hours.
- Minutes: 40 minutes need to be converted into hours. Since there are 60 minutes in an hour, we divide by 60:
[tex]\[ \frac{40}{60} \approx 0.6667 \, \text{hours} \][/tex]
- Seconds: 3.4181 seconds need to be converted into hours. Since there are 3600 seconds in an hour, we divide by 3600:
[tex]\[ \frac{3.4181}{3600} \approx 0.000949 \, \text{hours} \][/tex]
Now, add these values together to find the total time in hours:
[tex]\[ 2 + 0.6667 + 0.000949 \approx 2.6676 \, \text{hours} \][/tex]
Step 2: Calculate the average speed.
The distance of the race is 500 miles. To find the average speed, use the formula:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time in hours}} \][/tex]
[tex]\[ \text{Average speed} = \frac{500 \, \text{miles}}{2.6676 \, \text{hours}} \approx 187.433 \, \text{miles per hour} \][/tex]
Therefore, Tony Kanaan's average speed in the race was approximately 187.433 miles per hour when rounded to the thousandth of a mile per hour.
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