Question

Matt and Anna Killian are frequent fliers on​ Fast-n-Go Airlines. They often fly between two cities that are a distance of 1980 miles apart. On one particular​ trip, they flew into the wind and the trip took 5.5 hours. The return trip with the wind behind​ them, only took about 4.5 hours. Find the speed of the wind and the speed of the plane in still air.

Answer 1

y (plane speed) 400 miles/hr

x (wind speed) 40 miles/hr

Explanation:

going into the wind make the plane flew 5,5 hours to get 1980 miles, implies the real travel speed was

1980 / 5,5 = 360 miles/hours, and at the same time is the result of:

speed plane (y) in direction A to B plus wind speed (x) in direction B to A. Notice opposites direction speed, so we have:

y + (-x) = 360 (1)

The return fly took 4,5 hours so 1980/4,5 = 440 miles/ hours as the result

Y + x = 440 (2)

We have a two equation with two variables system, It could be solved for any of the procedures. We will use the substitution method.

From equation (1) y + (-x) = 360 y - x = 360 y = 360 + x (1)

In the second equation

y + x = 440 then we replace y for its value as function of x

(360 + x ) + x = 440

Solving for x 360 + 2x = 440 or 2x = 440 – 360

x (440 - 360)/2

x = 40 miles/hr

X (wind speed ) = 40 miles/hr

And replacing the value of x in eq. (1) y = 360 + 40 = 400

Y (plane speed) = 400 miles /hr