# RE1 | perplexity/sonar-pro | run 1

## Prompt

A train travels 240 miles in 3 hours, then 180 miles in 2 hours. What is its average speed for the entire trip? Show your work.

## Response

The train’s **average speed for the entire trip is 84 miles per hour**. This comes from dividing the *total distance* traveled by the *total time* for both parts of the journey.

## Step-by-step work

1. **Identify the distances for each leg of the trip**

- First part: 240 miles  
- Second part: 180 miles  

Total distance:
\[
\text{Total distance} = 240 + 180 = 420 \text{ miles}
\]

2. **Identify the times for each leg**

- First part: 3 hours  
- Second part: 2 hours  

Total time:
\[
\text{Total time} = 3 + 2 = 5 \text{ hours}
\]

3. **Use the average speed formula**

Average speed is defined as:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\]
This is the standard definition of average speed in physics.[Average Speed Formula](https://www.geeksforgeeks.org/physics/average-speed-formula/)

Substitute the values:
\[
\text{Average speed} = \frac{420 \text{ miles}}{5 \text{ hours}} = 84 \text{ miles per hour}
\]

So, the train’s **average speed over the entire 420-mile trip is 84 mph**.

Would you like to see a similar example where the speeds for each part are given instead of the distances and times?
