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 must determine the remaining distance and the time she has left to achieve her target average speed.

**Step 1: Determine the total distance and the distance already covered.**
The total length of the trail is 12 miles.
Marissa walked the first 4 miles and then the next 2 miles.
Distance covered = $4 + 2 = 6$ miles.

**Step 2: Determine the remaining distance.**
Remaining distance = Total distance - Distance covered
Remaining distance = $12 - 6 = 6$ miles.

**Step 3: Determine the total time allowed for the target average speed.**
Marissa wants an average speed of 4 miles per hour for the entire 12-mile trail.
Total time allowed = $\frac{\text{Total Distance}}{\text{Average Speed}}$
Total time allowed = $\frac{12 \text{ miles}}{4 \text{ mph}} = 3$ hours.

**Step 4: Determine the time already spent.**
She took 1 hour for the first part and another hour for the second part.
Time spent = $1 + 1 = 2$ hours.

**Step 5: Determine the remaining time available.**
Remaining time = Total time allowed - Time spent
Remaining time = $3 - 2 = 1$ hour.

**Step 6: Calculate the required speed for the remaining distance.**
She needs to cover the remaining 6 miles in the remaining 1 hour.
Required speed = $\frac{\text{Remaining Distance}}{\text{Remaining Time}}$
Required speed = $\frac{6 \text{ miles}}{1 \text{ hour}} = 6$ mph.

\boxed{6}