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

## 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 average the two speeds?

Each leg has a different speed: 240/3 = 80 mph and 180/2 = 90 mph. Averaging those gives 85 mph, which is wrong here — that shortcut only works when the *time* spent at each speed is equal. Since the train spent 3 hours at 80 mph and only 2 hours at 90 mph, the slower leg carries more weight, pulling the true average down to 84 mph.

Want to see how the answer changes if the legs are defined by equal distances instead of equal times (the harmonic mean case)?
