Two planes leave New Orleans at the same time. Plane A heads north and Plane B heads south. After 4 hours and 15 minutes, the two planes are 4568.75 miles apart. Also, Plane A is traveling 53 mph faster than Plane B.
At what speeds are the two planes traveling at?
How far did each plane travel?
If B's speed is x, the A's speed is x+53
Since distance = speed*time, we have
4.25(x + x+53) = 4568.75
To find the speeds at which the two planes are traveling, let's assign variables to the unknowns. Let's say the speed of Plane B is "x" mph. Since Plane A is traveling 53 mph faster than Plane B, we can say that the speed of Plane A is "x + 53" mph.
Now, to find the speeds, we need to use the formula Distance = Speed * Time.
For Plane A: Distance = (x + 53) * 4.25 (converting 4 hours and 15 minutes to decimal form)
For Plane B: Distance = x * 4.25
Since the total distance between the two planes is given as 4568.75 miles, we can set up the equation:
Distance of Plane A + Distance of Plane B = 4568.75
(x + 53) * 4.25 + x * 4.25 = 4568.75
Now, let's solve for x:
4.25x + 4.25x + 226.25 = 4568.75
8.5x = 4568.75 - 226.25
8.5x = 4342.50
x = 4342.50 / 8.5
x ≈ 511.47
Therefore, the speed of Plane B is approximately 511.47 mph. To find the speed of Plane A, we can substitute this value back into the equation:
Speed of Plane A = x + 53
Speed of Plane A ≈ 511.47 + 53
Speed of Plane A ≈ 564.47 mph
The two planes are traveling at approximately 511.47 mph and 564.47 mph, respectively.
To find out how far each plane traveled, we can substitute the speeds we just found into the distance formula:
Distance of Plane A = (564.47) * 4.25 ≈ 2401.22 miles
Distance of Plane B = (511.47) * 4.25 ≈ 2174.93 miles
Therefore, Plane A traveled approximately 2401.22 miles, and Plane B traveled approximately 2174.93 miles.