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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To find the speed Marissa needs to walk the remaining distance, we need to determine the total time available and the time remaining.

1.  **Calculate the total time required for the entire hike:**
    The total distance of the trail is 12 miles, and the target average speed is 4 miles per hour.
    $$ \text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} = \frac{12 \text{ miles}}{4 \text{ mph}} = 3 \text{ hours} $$

2.  **Calculate the distance and time already covered:**
    *   First leg: 4 miles in 1 hour.
    *   Second leg: 2 miles in 1 hour.
    *   Total distance covered so far: $4 + 2 = 6$ miles.
    *   Total time spent so far: $1 + 1 = 2$ hours.

3.  **Calculate the remaining distance and time:**
    *   Remaining distance: $12 \text{ miles (total)} - 6 \text{ miles (covered)} = 6$ miles.
    *   Remaining time: $3 \text{ hours (total)} - 2 \text{ hours (spent)} = 1$ hour.

4.  **Calculate the required speed for the remaining distance:**
    To cover the remaining 6 miles in the remaining 1 hour, the speed must be:
    $$ \text{Required Speed} = \frac{\text{Remaining Distance}}{\text{Remaining Time}} = \frac{6 \text{ miles}}{1 \text{ hour}} = 6 \text{ mph} $$

\boxed{6}