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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I need to find the speed Marissa needs to walk the remaining distance to achieve an average speed of 4 mph for the entire 12-mile trail.

Let me break down what I know:
- Total trail distance: 12 miles
- Time for first 4 miles: 1 hour
- Time for next 2 miles: 1 hour
- Desired average speed for entire trail: 4 mph

First, let me find how much time Marissa has total to complete the 12-mile trail at 4 mph:
Time = Distance ÷ Speed = 12 miles ÷ 4 mph = 3 hours

Next, let me calculate how much distance she has covered so far:
- First part: 4 miles
- Second part: 2 miles
- Total covered: 4 + 2 = 6 miles

So she has 12 - 6 = 6 miles remaining to hike.

Now I'll find how much time she has already spent:
- Time for first 4 miles: 1 hour
- Time for next 2 miles: 1 hour
- Total time so far: 1 + 1 = 2 hours

Since she needs 3 hours total and has already spent 2 hours, she has 3 - 2 = 1 hour remaining.

Therefore, to cover the remaining 6 miles in 1 hour, she needs to walk at:
Speed = Distance ÷ Time = 6 miles ÷ 1 hour = 6 mph

$\boxed{6}$