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 required speed for the remaining distance, we first determine the total time Marissa needs to complete the hike to achieve her target average speed.

The total distance of the trail is 12 miles, and she wants an average speed of 4 miles per hour. Using the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$, the total time required is:
$12 \text{ miles} \div 4 \text{ mph} = 3 \text{ hours}$.

Next, we calculate how much distance she has already covered and how much time she has already spent. She walked 4 miles in 1 hour, then 2 miles in another hour. So:
Distance covered = $4 + 2 = 6$ miles.
Time spent = $1 + 1 = 2$ hours.

Now, we find the remaining distance and the remaining time allowed:
Remaining distance = $12 - 6 = 6$ miles.
Remaining time = $3 - 2 = 1$ hour.

Finally, we calculate the speed she needs to maintain for the remaining distance:
$\text{Required speed} = \frac{\text{Remaining distance}}{\text{Remaining time}} = \frac{6 \text{ miles}}{1 \text{ hour}} = 6 \text{ mph}$.

\boxed{6}