# RE1 | anthropic/claude-opus-5 | 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**.

## Work

**Step 1 — Total distance**

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

**Step 2 — Total time**

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

**Step 3 — Apply the average speed formula**

\[ \text{Average speed} = \frac{\text{total distance}}{\text{total time}} = \frac{420}{5} = 84 \text{ mph} \]

## Why not just average the two speeds?

The individual leg speeds are 80 mph (240 ÷ 3) and 90 mph (180 ÷ 2). Their simple mean happens to be 85 mph, which is *not* the correct answer. Averaging speeds directly only works when the time spent at each speed is equal — here the train spends 3 hours at 80 mph and only 2 hours at 90 mph, so the slower leg carries more weight, pulling the true average down to 84 mph.

Would you like to see how this changes if the two legs covered equal distances instead of equal-ish times?
