Question 1005842

It took an airplane 2 hours to fly 600 miles against a headwind. The return trip with the wind took 1 2/3 hours. Find the speed of the plane with no wind and the windspeed. (Assume that both speeds remain constant.)

The speed of the plane is ____ MPH
The Windspeed is ____ MPH
<pre>Let speed of plane in still air, and speed of wind speed, be S and W, respectively
Then total speed when going against the wind = S - W
Also, total speed when going with the wind = S + W
Therefore, we can say that: {{{S - W = 600/2}}}, or S – W = 300 ---- eq (i)
And, {{{S + W = 600/(1&2/3)}}}, or {{{S + W = 600/(5/3)}}}, or S + W = 360 ---------- eq (ii)
2S = 660 ------- Adding eqs (i) & (ii)
S, or speed in still air = {{{660/2}}}, or {{{highlight_green(330)}}} mph
330 – W = 300 -------- Substituting 330 for S in eq (i) 
- W = 300 – 330
- W = - 30
W, or wind speed = {{{(- 30)/(- 1)}}}, or {{{highlight_green(30)}}} mph