Sure! Let's go through the problem step by step to find Nancy's average speed on her trip to Paris.
1. Understand the information given:
- The time taken to travel to Paris (going there) is 7 hours.
- The time taken to return from Paris is 6 hours.
- The average speed on the return trip is 45 miles per hour (mph).
2. Calculate the distance of the return trip:
- Using the formula for distance, which is:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
- We know the speed (45 mph) and the time (6 hours) for the return trip.
- So, the distance for the return trip is:
[tex]\[
\text{Distance (return trip)} = 45\ \text{mph} \times 6\ \text{hours} = 270\ \text{miles}
\][/tex]
3. The distance traveled to Paris is the same as the distance for the return trip:
- Therefore, the distance for the trip to Paris is also 270 miles.
4. Calculate the average speed for the trip to Paris:
- Using the formula for speed, which is:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
- We now know the distance (270 miles) and the time taken (7 hours) for the trip to Paris.
- So, the average speed for the trip to Paris is:
[tex]\[
\text{Average Speed (trip to Paris)} = \frac{270\ \text{miles}}{7\ \text{hours}} \approx 38.57\ \text{mph}
\][/tex]
Thus, Nancy’s average speed on her trip to Paris was approximately [tex]\(38.57\)[/tex] miles per hour.
