Question

If a plane can travel 490 miles per hour with the wind and 390 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.

Answer 1

The speed of the plane in still air is 440 miles per hour and the speed of the wind is 50 miles per hour. Figured as follows:

Speed of the plane traveling with the wind subtracted by the speed of the plane traveling against the wind (490 minus 390) equals 100. Divide 100 by the number of directions traveled (with and against the wind); (100 divided by 2) equals 50. Thus the speed of the wind is 50 miles per hour.

If no wind was acting on the plane then the average of the difference of the speeds recorded would be the planes speed in still air. (490 minus 390 equals 100 divided by 2 equals 50 plus 390 equals 440 miles per hour).

Answer 2

Let the speed of plane in still air be x and that wind be y
therefore:
x+y=490
x-y=390
next we solve for the values of x and y, first we add the above equations. This will give us:
2x=880
x=880/2
x=440 miles per hour.
substituting the value of x in one of the equations and solving for y we get:
440+y=490
y=490-440
y=50 miles per hour