Mattie evans drove 150 miles in the same amount of time that it took a turbopropeller plane to travel 600 miles. the speed of the plane was 150 mph faster than the speed of the car. find the speed of the plane.

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

side 1: t - 1

side 2: t + 1

side 3: 4

side 1 + side 2 > side 3   &  side 2 + side 3 > side 1   &  side 3 + side 1 > side 2

(t - 1)   + (t + 1)   >   4              (t + 1)   +   (4)    >   (t - 1)            (4)     + (t - 1)  >  (t + 1)

       2t > 4                                  t + 5          >   t - 1                      t + 3       >   t + 1

         t > 2                                       5 > -1   (TRUE)                            3 > 1 (TRUE)

t > 2