Flying with a tailwind a plane averaged 158 km/h. On the return trip the plane averaged 112 km/h with same wind. Find wind & plane speed in still air.

Question

I got as far as  plane speed + wind  = 158 and plane speed - wind = 112.

But I don't know how to solve the problem.

Answer 1

You need to name variables for plane speed and wind speed.  For example, I will name them:

x = Plane speed

y = Wind speed

Now you can create two equations in two variables

x + y = 158

x - y =112

This is a good problem for elimination method since you already have one equation with positive y and the other with negative y

x + y = 158
x - y = 112
2x    = 270

x = 135

Now substitute the value into either equation to solve for y

x + y - 158

135 + y = 158

y = 23

 

Answer 2

Hi Roxi -- here's another angle: during a round trip, the wind effect cancels out, much like going downhill and returning uphill. Your "still air" speed would be the average for the round trip = (158+112)/2= 135mph. Therefore, a 23-mph wind boosted the plane to 158 and slowed it to 112.  Best regards ma'am ...