Question

Mattie Evans drove 200 miles in the same amount of time that it took a turbopropeller plane to travel 950 miles. The speed of the plane was 150 mph faster than th

speed of the car. Find the speed of the plane.
The speed of the plane was mph.
(Simplify your answer.)

Answer 1

The speed of the plane is 190 mph. This was calculated using the relationship between distance, speed, and time for both the car and the plane, and knowing that the plane's speed was 150 mph faster than the car's speed.

Step-by-step explanation:

To find the speed of the plane, we need to set up an equation using the fact that Mattie Evans drove 200 miles in the same amount of time it took the plane to travel 950 miles. Let's denote the speed of Mattie's car as v and the speed of the plane as v + 150 mph since we know that the plane was 150 mph faster than the car.

Next, we use the relationship Distance = Speed × Time. Both the car and plane travelled for the same time, so:

• Time for car = Time for plane
• 200 / v = 950 / (v + 150)

Now, cross multiply to solve for v:

1. 200(v + 150) = 950v
2. 200v + 30000 = 950v
3. 750v = 30000
4. v = 30000 / 750
5. v = 40 mph for the speed of the car

To find the speed of the plane, we add 150 mph to the car's speed:

• Speed of the plane = v + 150
• Speed of the plane = 40 mph + 150 mph
• Speed of the plane = 190 mph

Answer 2

speed of the plane = 190 mph

Step-by-step explanation:

Let x = speed of the plane, then speed of the car = x - 150

time = 200/(x - 150) = 950/x

Divide by 50 on both sides, get

4/(x - 150) = 19/x

Cross multiply:

4x = 19(x - 150)

4x = 19x - 19*150

15x = 19*150

x = 19*150/15 = 190