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could someone please check my answer for this problem. All of my work and equations are clearly presented in the picture attached below. (If my answer is wrong, please give me pointers on how I could obtain the correct solution).

Thanks!

Problem 5:

On their way to play soccer in the World Cup, Mia and Brandi get stranded at O'Hare Airport in Chicago because of bad weather. Late at night, with nobody else around, they decide to have a race to see who is faster. They run down to a particular point, then turn around and return to their starting point. That race turns out to be a tie. They race again, this time with Mia running on a moving sidewalk. They start at the same time, run east at top speed a distance L through the airport terminal, and then turn around and run west back to the starting point. Brandi runs at a constant speed v, while Mia runs on a moving sidewalk that travels at a constant speed of v/3. Mia runs at a constant speed v relative to the moving sidewalk. Neglect the time it takes the women to turn around at the halfway point. Let's say that v = 8.00 m/s and L = 48.0 m.

(a) Mia reaches the turnaround point first, because she starts off running on the moving sidewalk in the direction the sidewalk is moving. What is the distance between the two women when Mia is at the turnaround point?

(b) After Mia turns around, she is running opposite to the direction the moving sidewalk is moving. What is the distance between the two women when Brandi is at the turnaround point?

(c) What is the distance between the two women when the winner of the race reaches the finish line?