Question 299199
An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?


Let the plane's speed be S, and the wind's speed W


Since it took 4 hours against a headwind to fly 1,200 miles, then speed = {{{1200/4}}} or 300 mph.


This means that the speed of the plane - windspeed = 300 mph, or, S - W = 300


Since it took 3 hours with the headwind to fly 1,200 miles, then speed = {{{1200/3}}} or 400 mph.


This means that the speed of the plane + windspeed = 400 mph, or, S + W = 400


S - W = 300 ------ (i)
S + W = 400 ------ (ii)


2S = 700 ------- Adding eqs (i) & (ii)


S, or speed of plane = {{{700/2}}} or {{{highlight_green(350)}}} mph


Substituting 350 for S in eq (i), we get:


350 - W = 300


- W = - 50


W, or windspeed = {{{(-50)/-1}}} or {{{highlight_green(50)}}} mph