gsm8k-0019

# GSM8K Problem 20

Marissa is hiking a 12-mile trail. She took 1 hour to walk the first 4 miles, then another hour to walk the next two miles. If she wants her average speed to be 4 miles per hour, what speed (in miles per hour) does she need to walk the remaining distance?

Reason step by step, then give ONLY the final answer on the last line as \boxed{ANSWER}.

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We are given:

- Total trail distance: **12 miles**
- Marissa wants an **average speed of 4 miles per hour** over the entire hike.
- She has already walked:
  - First 4 miles in 1 hour
  - Next 2 miles in 1 hour  
  → So far, she has walked **6 miles in 2 hours**

We need to find:  
What speed must she walk the **remaining distance** (12 − 6 = **6 miles**) to achieve an average speed of **4 mph** overall?

---

### Step 1: Total time needed for average speed of 4 mph over 12 miles

Average speed = total distance / total time  
So:

$$
\text{Total time} = \frac{\text{Total distance}}{\text{Average speed}} = \frac{12}{4} = 3 \text{ hours}
$$

She has already spent **2 hours**, so she has **1 hour left** to complete the remaining 6 miles.

### Step 2: Required speed for remaining 6 miles in 1 hour

$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{6}{1} = 6 \text{ mph}
$$

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\boxed{6}