Two cars are approaching an intersection at the origin in the figure below. One car is 15 miles north of the intersection and traveling at a rate of 45 mph. The other car is 24 miles east of the intersection and traveling at a rate of 52 mph.

1. What are the parametric equations that represent the position of the car approaching from the north?
2. What are the parametric equations that represent the position of the car approaching from the east?
3. Select "Animate" graph Style and "Simultaneous" graph Order for the equations in Questions 1 and 2, simulate the movement of the cars using the window below, and answer the question that follows.

tmin = 0	xmin = -5	ymin = -5
tmax = 0.4	xmax = 40	ymax = 20
tstep = 0.01	xscl = 5	yscl = 5

According to the simulation, which car reaches the intersection first?

4. Define a function that represents the distance between the two cars.
5. How fast is the distance between the cars changing at t = 0.25 hours?

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