# RE1 | deepseek/deepseek-v4-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 average speed for the entire trip is 84 miles per hour.

Here's the step-by-step calculation:

**Step 1: Find the total distance traveled.**
First segment: 240 miles
Second segment: 180 miles
Total distance = 240 + 180 = 420 miles

**Step 2: Find the total time taken.**
First segment: 3 hours
Second segment: 2 hours
Total time = 3 + 2 = 5 hours

**Step 3: Apply the average speed formula.**

\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\]

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

---

A common mistake is to simply average the two speeds (\( \frac{80 + 90}{2} = 85 \text{ mph} \)), but that only works when the time intervals are equal. Since the train spent more time traveling at 80 mph (3 hours) than at 90 mph (2 hours), the true average speed is weighted toward the slower segment, producing the correct result of 84 mph.

Would you like to try a similar problem involving three or more segments, where the time intervals vary?
