Mattie evans drove 80 miles in the same amount of time that it took a turbopropeller plane to travel 400 miles. the speed of the plane was 160 mph faster than the speed of the car. find the speed of the plane.

The plane was travelling 164 mph.

We begin with the formula d=rt, where d is distance, r is rate (speed) and t is time.  The time is the same for both vehicles, so we will solve the formula for t:

d=rt

Divide both sides by r:
d/r = t

We know that the time is the same for both vehicles so this sets up a proportion:
d/r = d/r

The car travels 80 miles at an unknown speed, x:
80/x = d/r

The plane travels 400 miles at 160 mph faster than the unknown speed:
80/x = 400/(x+160)

Cross multiply:
80(x+160) = 400*x
80x + 1280 = 400x

Subtract 80x from both sides:
80x + 1280 - 80x = 400x - 80x
1280 = 320x

Divide both sides by 320:
1280/320 = 320x/320
4 = x

The car travels at 4 mph; the plane travels at 4+160 = 164 mph.