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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Let's break down the problem step by step.

1. **Total Distance and Desired Average Speed:**
   - Total distance of the trail: 12 miles.
   - Desired average speed: 4 miles per hour.

2. **Calculate Total Time Required for Desired Average Speed:**
   - Average speed = Total distance / Total time.
   - So, Total time = Total distance / Average speed = 12 miles / 4 mph = 3 hours.

3. **Time Already Spent Hiking:**
   - Time for first 4 miles: 1 hour.
   - Time for next 2 miles: 1 hour.
   - Total time spent so far: 1 hour + 1 hour = 2 hours.

4. **Remaining Time to Achieve Desired Average Speed:**
   - Total time required: 3 hours.
   - Time already spent: 2 hours.
   - Remaining time: 3 hours - 2 hours = 1 hour.

5. **Remaining Distance to Hike:**
   - Total distance: 12 miles.
   - Distance already hiked: 4 miles + 2 miles = 6 miles.
   - Remaining distance: 12 miles - 6 miles = 6 miles.

6. **Calculate Required Speed for Remaining Distance:**
   - Required speed = Remaining distance / Remaining time = 6 miles / 1 hour = 6 mph.

Therefore, Marissa needs to walk the remaining distance at a speed of 6 miles per hour to achieve her desired average speed.

$\boxed{6}$