Final answer:
By setting up equations and solving, Nina's average speed is 20.5 km/h and Rita's is 25.5 km/h. However, this does not match any of the provided answer choices, suggesting there might be an issue with the options given in the question.
Step-by-step explanation:
To solve the problem, we need to set up equations based on the information provided. Let's assume Nina's average speed is x km/h. Therefore, Rita's average speed is x + 5 km/h. They passed each other after 2 hours (from 11:50 am to 1:50 pm). So Nina covered 2x kilometers, and Rita covered 2(x + 5) kilometers in that time.
The total distance they covered when they met would be equal to the distance between the park and the museum, which is 92 km:
2x + 2(x + 5) = 92
We add the distances covered by both:
2x + 2x + 10 = 92
4x + 10 = 92
Now, we subtract 10 from both sides:
4x = 82
Then we divide both sides by 4 to find x:
x = 20.5
As Rita's speed was 5 km/h faster than Nina's, we calculate Rita's average speed:
Rita's speed = 20.5 + 5 = 25.5 km/h
However, this is not one of the options provided, so we should check back our calculations to make sure there wasn't a mistake. Upon review, it appears that the values provided in the question may be incorrect, as the solution does not match any of the answer choices.