To find the total time it takes for Megan to get to work, we need to break her commute into two parts: the 8-mile drive and the 21-mile train ride. Let's use the given expression and plug in Megan's average driving speed.
Given:
- Megan's drive distance is [tex]\( 8 \)[/tex] miles.
- Megan's train ride distance is [tex]\( 21 \)[/tex] miles.
- Megan's average driving speed is [tex]\( 45 \)[/tex] miles/hour.
- The average speed of the train is [tex]\( 20 \)[/tex] miles/hour more than Megan's driving speed.
1. Calculate the driving time:
- Megan’s driving speed is [tex]\( 45 \)[/tex] miles/hour.
- Distance for the drive = [tex]\( 8 \)[/tex] miles.
- The driving time [tex]\( (T_{drive}) \)[/tex] can be calculated using the formula:
[tex]\[
T_{drive} = \frac{\text{distance}}{\text{speed}} = \frac{8}{45}
\][/tex]
- So, the driving time is approximately [tex]\( 0.1778 \)[/tex] hours.
2. Calculate the train ride speed:
- The train speed [tex]\( = 45 + 20 = 65 \)[/tex] miles/hour.
3. Calculate the train ride time:
- Distance for the train ride = [tex]\( 21 \)[/tex] miles.
- The train ride time [tex]\( (T_{train}) \)[/tex] can be calculated using the formula:
[tex]\[
T_{train} = \frac{\text{distance}}{\text{speed}} = \frac{21}{65}
\][/tex]
- So, the train ride time is approximately [tex]\( 0.3231 \)[/tex] hours.
4. Calculate the total travel time:
- Total time [tex]\( = T_{drive} + T_{train} \)[/tex]:
[tex]\[
\text{Total time} = 0.1778 + 0.3231 = 0.5009 \text{ hours}
\][/tex]
5. Conclusion:
- When Megan drives at an average speed of 45 miles/hour, her total commute time to work, including both the driving and train ride, is approximately [tex]\( 0.5009 \)[/tex] hours.
- Specifically, it takes her approximately [tex]\( 0.1778 \)[/tex] hours for the 8-mile drive and [tex]\( 0.3231 \)[/tex] hours for the 21-mile train ride.
