Sure! Let's break down this problem step by step to determine the total distance the self-driving car traveled.
1. Convert Mixed Numbers to Improper Fractions:
The time the car drove during the first leg is given as [tex]\(1 \frac{1}{5}\)[/tex] hours.
- To convert [tex]\(1 \frac{1}{5}\)[/tex] to an improper fraction: [tex]\(1 + \frac{1}{5} = 1.2\)[/tex] hours.
The time the car drove during the second leg is given as [tex]\(3 \frac{1}{2}\)[/tex] hours.
- To convert [tex]\(3 \frac{1}{2}\)[/tex] to an improper fraction: [tex]\(3 + \frac{1}{2} = 3.5\)[/tex] hours.
2. Calculate the Distance for Each Leg of the Trip:
The speed during the first leg of the journey was 70.5 miles per hour.
- Distance for the first leg: [tex]\( \text{time} \times \text{speed} = 1.2 \text{ hours} \times 70.5 \text{ miles per hour} = 84.6 \text{ miles}\)[/tex].
The speed during the second leg of the journey was 62.4 miles per hour.
- Distance for the second leg: [tex]\( \text{time} \times \text{speed} = 3.5 \text{ hours} \times 62.4 \text{ miles per hour} = 218.4 \text{ miles}\)[/tex].
3. Calculate the Total Distance Traveled:
To find the total distance traveled, simply add the distances from both legs of the journey.
[tex]\[
84.6 \text{ miles} + 218.4 \text{ miles} = 303.0 \text{ miles}
\][/tex]
Therefore, the car traveled a total distance of 303.0 miles.
