# RE1 | google/gemini-3.6-flash | 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 average speed of the train for the entire trip is 84 miles per hour. This value is calculated by dividing the total distance traveled across both legs of the journey by the total time elapsed.

## Step-by-Step Calculation

**1. Calculate the Total Distance**
Sum the distances of each leg of the trip:
\[ d_{\text{total}} = 240 \text{ miles} + 180 \text{ miles} = 420 \text{ miles} \]

**2. Calculate the Total Time**
Sum the time taken for each leg:
\[ t_{\text{total}} = 3 \text{ hours} + 2 \text{ hours} = 5 \text{ hours} \]

**3. Calculate the Average Speed**
Apply the average speed formula \( v_{\text{avg}} = \frac{d_{\text{total}}}{t_{\text{total}}} \):
\[ v_{\text{avg}} = \frac{420 \text{ miles}}{5 \text{ hours}} = 84 \text{ mph} \]

Would you like to calculate how long it would take the train to complete another distance at this same average speed?
