Mattie Evans drove 300 miles in the same amount of time that it took a turbo propeller plane to travel 1300 miles. The speed of the plane was 200 mph faster than the speed of the car.Find the speed of the plane.
250.33
To find the speed of the plane, we need to set up a system of equations based on the given information.
Let's assume that the speed of the car is "x" mph. Since the plane is 200 mph faster than the car, the speed of the plane would be "x + 200" mph.
We can use the formula "distance = speed × time" to set up two equations.
For the car: 300 miles = x mph × time
For the plane: 1300 miles = (x + 200) mph × time
Since we are given that the car and the plane traveled the same amount of time, we can set up the equations as follows:
300 = x × time
1300 = (x + 200) × time
Now, we can solve this system of equations to find the speed of the plane.
Divide the second equation by the first equation to eliminate the time variable:
1300/300 = (x + 200)/x
Simplifying, we get:
13/3 = (x + 200)/x
Cross multiply to solve for x:
13x = 3(x + 200)
13x = 3x + 600
Subtract 3x from both sides:
10x = 600
Divide both sides by 10:
x = 60
So, the speed of the car is 60 mph.
To find the speed of the plane, substitute the value of x into the expression x + 200:
60 + 200 = 260
Therefore, the speed of the plane is 260 mph.