The speed of the plane is 200 mph.
We start out with the formula d=rt, where d is distance, r is rate (speed) and t is time. We know the time is the same for both vehicles, so we will solve this formula for t:
d=rt
Divide both sides by r:
d/r = t
Since the time is the same, we will have a proportion in the form
d/r = d/r
The speed of the car is x, and it travels 150 miles. The speed of the plane is 150 faster than x, or x+150, and it travels 600 miles:
150/x = 600/(x+150)
Cross multiplying we have:
150(x+150) = 600*x
150x + 22500 = 600x
Subtract 150x from both sides:
150x + 22500 - 150x = 600x - 150x
22500 = 450x
Divide both sides by 450:
22500/450 = 450x/450
50 = x
The speed of the car is 50, and the speed of the plane is 50+150 = 200