They will meet at 1 PM, 6 miles from the trailhead and the correct option is C.
Edna leaves the trailhead at 7 AM and needs to hike 12 miles to the lake. Maria hikes at a rate of 1/2 mile per hour, and starts hiking from the lake at the same time as Edna.
We can calculate the time it takes Edna to reach the lake by dividing the distance by Maria's rate:
edna_time_to_lake = edna_distance / maria_rate
edna_time_to_lake = 12 miles / 0.5 miles per hour
edna_time_to_lake = 24 hours
Maria starts hiking at the same time as Edna, so she has been hiking for 24 hours when they meet. We can calculate the distance Maria has traveled by multiplying her rate by the time she has been hiking:
maria_distance_traveled = maria_rate * maria_time_hiking
maria_distance_traveled = 0.5 miles per hour * 24 hours
maria_distance_traveled = 12 miles
Since Maria has traveled 12 miles and Edna has traveled 12 miles, they must meet at the lake.
We can calculate the total time it takes for them to meet by adding the time it takes Edna to reach the lake and the time it takes Maria to reach the trailhead:
total_time = edna_time_to_lake + maria_time_to_trailhead
total_time = 24 hours + 24 hours
total_time = 48 hours
Converting the total time to hours and minutes, we get:
hours, minutes = divmod(total_time, 1)
hours = 48 // 1
minutes = 48 % 1 * 60
hours = 48
minutes = 0
Therefore, they will meet at 48 PM, 0 minutes past the hour, at the lake.
So the answer is At 1 PM, 9 miles from the trailhead and the correct option is C.