At noon, Car A is 10 km south of a straight east–west highway intersection and is traveling north toward the intersection at a constant speed of 60 km/h. At the same moment, Car B is 15 km west of the intersection and is traveling east toward the intersection at a constant speed of 45 km/h.
Let x(t) be the east–west distance (in kilometers) of Car B from the intersection at time t hours after noon (with x>0 east of the intersection), and let y(t) be the north–south distance (in kilometers) of Car A from the intersection at time t hours after noon (with y>0 north of the intersection). Define s(t) to be the straight-line distance (in kilometers) between the two cars at time t.
a. Calculate the instantaneous rate of change dtds at 12:30 p.m. Include units in your answer and state whether the distance between the cars is increasing or decreasing at that time.