Sure, let's solve this step-by-step.
1. Convert mixed numbers into improper fractions (or decimals) where necessary:
- The car travels [tex]\( 30 \frac{1}{5} \)[/tex] miles. This mixed number can be written as:
[tex]\[
30 + \frac{1}{5} = 30.2 \text{ miles}
\][/tex]
2. Identify the time travelled:
- The car travels for [tex]\(\frac{2}{3}\)[/tex] of an hour. This is already a fraction and can remain as such, but for easier division, we will convert it to a decimal:
[tex]\[
\frac{2}{3} \approx 0.6667 \text{ hours}
\][/tex]
3. Calculate the average speed using the formula:
[tex]\[
\text{Average Speed} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}
\][/tex]
- Here, the total distance traveled is [tex]\(30.2\)[/tex] miles and the total time taken is [tex]\(0.6667\)[/tex] hours.
4. Perform the division:
[tex]\[
\text{Average Speed} = \frac{30.2 \text{ miles}}{0.6667 \text{ hours}} \approx 45.30 \text{ miles per hour}
\][/tex]
Therefore, the car's average speed is approximately [tex]\(45.3\)[/tex] miles per hour.
