An airplane takes off from an airport and takes 6.5 hours to fly west (against the wind current) 2600 miles. The return trip (with the wind current) takes 5.2 hours. Find the airspeed and the wind speed.

v-c = 2600 / 6.5

v+c = 2600 / 5.2
----------------- add
2 v = 400 + 500 = 900
v = 450

450 - c = 400
c = 50

To find the airspeed and the wind speed, we can set up a system of equations based on the given information.

Let's assume that the airspeed of the airplane (the speed of the plane in still air) is represented by "x" and the wind speed is represented by "y".

We can use the formula: Distance = Speed × Time

For the westward trip (against the wind current):
Distance = 2600 miles
Time = 6.5 hours
Speed = Airspeed - Wind speed (since they are travelling against the wind)

Using the formula, we get:
2600 = (x - y) × 6.5 ---- Equation 1

For the return trip (with the wind current):
Distance = 2600 miles (same as before)
Time = 5.2 hours
Speed = Airspeed + Wind speed (since they are travelling with the wind)

Using the formula, we get:
2600 = (x + y) × 5.2 ---- Equation 2

Now we have a system of equations:
2600 = (x - y) × 6.5 ---- Equation 1
2600 = (x + y) × 5.2 ---- Equation 2

We can solve this system of equations to find the values of x (airspeed) and y (wind speed).

First, let's simplify Equation 1 by dividing both sides by 6.5:
400 = x - y ---- Equation 1 simplified

Next, let's simplify Equation 2 by dividing both sides by 5.2:
500 = x + y ---- Equation 2 simplified

Now we have a system of simplified equations:
400 = x - y ---- Equation 1 simplified
500 = x + y ---- Equation 2 simplified

We can add these two equations together to eliminate the variable y:
400 + 500 = (x - y) + (x + y)
900 = 2x

Dividing both sides of the equation by 2, we find:
x = 450

Now that we know the airspeed is 450 mph, we can substitute this value back into one of the simplified equations to find the wind speed.

Using Equation 2 simplified:
500 = 450 + y

Subtracting 450 from both sides of the equation:
B = 50

Therefore, the airspeed of the airplane is 450 mph and the wind speed is 50 mph.