# RE1 | perplexity/sonar-pro | run 2

## 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 (mph)**. This comes from dividing the *total distance* traveled by the *total time* taken.

## Step-by-step work

**1. Find the total distance**

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

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

Average speed is defined as total distance divided by total time.[Average Speed Definition](https://www.cuemath.com/average-speed-formula/)

**2. Find the total time**

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

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

Average speed uses this total time for the whole journey.[Average Speed Steps](https://thirdspacelearning.com/us/math-resources/topic-guides/ratio-and-proportion/average-speed-formula/)

**3. Compute the average speed**

Use the formula \(\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}\).[Speed = Distance/Time](https://www.calculatorsoup.com/calculators/math/speed-distance-time-calculator.php)

\[
\text{Average speed} = \frac{420\ \text{miles}}{5\ \text{hours}} = 84\ \text{mph}
\]

So, the train’s **average speed** for the entire trip is **84 mph**.

Would you like to see a similar problem where the speeds change but the distances are the same, so you can compare how average speed behaves?
