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}.

<!-- imported from openai/gsm8k (test) -->

To find the required speed for the remaining distance, we need to determine the total time Marissa has already spent and the total distance she has yet to travel.

1.  **Calculate the total distance of the trail:**
    The trail is 12 miles long.

2.  **Calculate the distance already traveled:**
    Marissa walked 4 miles in the first hour and 2 miles in the second hour.
    $$4 \text{ miles} + 2 \text{ miles} = 6 \text{ miles}$$

3.  **Calculate the remaining distance:**
    Subtract the distance already traveled from the total distance.
    $$12 \text{ miles} - 6 \text{ miles} = 6 \text{ miles}$$

4.  **Calculate the total time already spent:**
    She walked for 1 hour for the first part and 1 hour for the second part.
    $$1 \text{ hour} + 1 \text{ hour} = 2 \text{ hours}$$

5.  **Determine the total time allowed to finish the trail:**
    Her goal is to have an average speed of 4 miles per hour for the entire 12-mile hike.
    $$\text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} = \frac{12 \text{ miles}}{4 \text{ mph}} = 3 \text{ hours}$$

6.  **Calculate the time remaining for the last 6 miles:**
    Subtract the time already spent from the total time allowed.
    $$3 \text{ hours} - 2 \text{ hours} = 1 \text{ hour}$$

7.  **Calculate the required speed for the remaining distance:**
    Divide the remaining distance by the remaining time.
    $$\text{Speed} = \frac{6 \text{ miles}}{1 \text{ hour}} = 6 \text{ mph}$$

\boxed{6}