A traveler flies from Charlotte, North Caroline to Los Angeles, California. At the same time, another traveler flies from Lost Angeles to Charlotte. The air speed of each plane is the same. The ground speed of the first plane is 550 mi/hr and the ground speed of the second plane is 495 mi/hr. What is the air speed? What is the wind speed?
(idk what the hell is going on with this question)
Let the air speed of the plane be x mph
let the wind speed by y mph
so for LA to C plane: x - y = 495
C to LA plane: x + y = 550
add them 2x = 1045
x = 522.5
then y = 27.5
speed of plane in still air = 522.5 mph
speed of wind = 27.5 mph
Btw, for most of the time, winds come from the west and blow east ,
so the plane going from LA to C should be the faster.
(remember those prevailing westerlies from geography class ?)
To solve this problem, we can use the concept of relative velocities. Let's denote the airspeed of both planes as "a" (in miles per hour) and the wind speed as "w" (in miles per hour).
The first step is to understand the concept of ground speed. Ground speed is the actual speed at which an aircraft is moving over the ground. It is a combination of the aircraft's airspeed and the effect of the wind.
For the first plane, we are given that its ground speed is 550 mph. Since its airspeed is "a," and the wind speed is "w," we can write the equation for the first plane's ground speed as follows:
Ground speed of the first plane = Airspeed of the first plane + Wind speed
550 mph = a mph + w mph (Equation 1)
For the second plane, we are given that its ground speed is 495 mph. Using the same logic as above, we can write the equation for the second plane's ground speed as follows:
Ground speed of the second plane = Airspeed of the second plane - Wind speed
495 mph = a mph - w mph (Equation 2)
Now, we have a system of equations with two unknowns (a and w). We can solve this system of equations to find the values of a and w.
To eliminate w, let's add Equation 1 and Equation 2:
(550 mph) + (495 mph) = (a mph + w mph) + (a mph - w mph)
1045 mph = 2a mph
Dividing both sides by 2:
a mph = 1045 mph / 2
a mph = 522.5 mph
So, the airspeed of both planes is 522.5 mph.
Now, we can substitute this value of a into Equation 1 to find the wind speed (w):
550 mph = 522.5 mph + w mph
Subtracting 522.5 mph from both sides:
550 mph - 522.5 mph = w mph
w mph = 27.5 mph
Therefore, the air speed of the planes is 522.5 mph, and the wind speed is 27.5 mph.
To solve this problem, we can use the concept of relative velocity. Let's assume the airspeed of both planes is 'a' and the wind speed is 'w'. When the first plane is flying from Charlotte to Los Angeles, it will be flying against the wind, so its effective ground speed will be the airspeed minus the wind speed (a - w). On the other hand, when the second plane is flying from Los Angeles to Charlotte, it will be flying with the wind, so its effective ground speed will be the airspeed plus the wind speed (a + w).
Given that the ground speed of the first plane is 550 mi/hr, we can equate it to the airspeed minus the wind speed: (a - w) = 550. Similarly, for the second plane with a ground speed of 495 mi/hr, we have (a + w) = 495.
Now we can solve these two equations simultaneously to find the values of 'a' and 'w'. Adding the two equations, we get:
(a - w) + (a + w) = 550 + 495
2a = 1045
a = 522.5
So, the airspeed of each plane is 522.5 mi/hr.
Substituting this value into one of the original equations:
(a - w) = 550
(522.5 - w) = 550
w = 522.5 - 550
w = -27.5
The wind speed is -27.5 mi/hr.
It's essential to note that in this scenario, a negative wind speed indicates that the wind is blowing against the direction of the first plane.