an airplane flew for 423 hours with a 255kmh tail wind the r

an airplane flew for 4.23 hours with a 25.5-km/h tail wind. the return flight against the same wind took 4.97 hours. find the speed of the plain in still air.

Solution

let the rate of airplane on the trip going = x+25.5km
Let the rate returning =x-25.5km
the distance is the same both ways,
using rate*time=distance, we have two equations:
(x+25.5)*4.23=d
(x-25.5)*4.97=d
Set them equal to one another,
(x+25.5)*4.23= (x-25.5)*4.97
4.23x+107.865=4.97x-126.735
subtract 4.23x and add 126.735 to both sides:
234.6=.74x
divide by .74
317.027=x
the airplane traveled 317.02kmh in still air.