Mattie Evans drove 250 miles in the same amount of time that it took a turbopropeller plane to travel 1250 miles. The speed of the plane was 200 mph faster than the speed of the car. Find the speed of the plane
its 450 mph
Speed = distance/time
time = distance/speed
Let x = plane speed and y = driving speed
y = x + 200
250/x = 1250/y
Substitute x + 200 for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
Car speed = X-mi/h,
Plane speed = (X + 200) mi/h,
Eq1: d1 = X*t = 250 mi,
t = 250 / X,
Eq2: d2 = (X + 200)t = 1250 mi.
Substitute 250 / X for t in Eq2:
(X + 200)250/X = 1250,
250 + 50000/X = 1250,
50000 / X = 1250 - 250,
50000 / X = 1000,
Cross multiply:
1000X = 50000,
X = 50000 / 1000 = 50 mi/h = car speed.
(X + 200) = 250 mi/h = plane speed.
To solve this problem, we can set up a simple equation. Let's say the speed of the car is "x" miles per hour. According to the problem, the plane's speed is 200 mph faster than the car, so the plane's speed is "x + 200" miles per hour.
Now, to find the time it took for both the car and the plane to travel their respective distances, we can use the formula "distance = speed × time." We know that the car traveled 250 miles and the plane traveled 1250 miles, so we can set up the following equations:
For the car: 250 = x × time
For the plane: 1250 = (x + 200) × time
Since the time it took for both the car and the plane to travel their distances is the same, we can set these two equations equal to each other:
x × time = (x + 200) × time
Now, we can cancel out the "time" factor on both sides of the equation since the time is the same in both cases:
x = x + 200
By simplifying this equation, we can solve for x, which is the speed of the car:
x - x = 200
0 = 200
This equation has no solution, which means there is an error in the given information or the problem itself. Please double-check the provided numbers or provide additional information if necessary.