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 out the speed Marissa needs to walk the remaining distance to achieve an average speed of 4 miles per hour for the entire 12-mile hike, we need to calculate the total time she has left to complete the hike after walking the first 6 miles.

First, let's find out how much time she has already spent walking the first 6 miles:

- 1 hour for the first 4 miles
- 1 hour for the next 2 miles

Total time spent so far = 1 + 1 = 2 hours

Marissa wants her average speed for the entire hike to be 4 miles per hour. The formula for average speed is:

Average Speed = Total Distance / Total Time

We know the Total Distance is 12 miles, and we want the Average Speed to be 4 miles per hour. So, we can rearrange the formula to find the Total Time:

Total Time = Total Distance / Average Speed
Total Time = 12 miles / 4 mph
Total Time = 3 hours

Marissa has already spent 2 hours walking, so she has 1 hour left to complete the hike (3 hours total - 2 hours spent = 1 hour left).

Now we need to find out the speed she needs to walk the remaining 6 miles in 1 hour to achieve her desired average speed.

Speed = Distance / Time
Speed = 6 miles / 1 hour
Speed = 6 mph

Marissa needs to walk the remaining 6 miles at a speed of 6 miles per hour to achieve an average speed of 4 miles per hour for the entire hike.

\boxed{6}