Question

A plane has a speed of p km/h in still air. It makes around trip flying with and against the wind of w km/h.Show that its average speed is p^2-w^2/p km/h

Answer 1

time with the wind = D/(p+w) , where D is the distance traveled
time against the wind = D/(p-w)

total time = D/(p+w) + D/(p-w)
= (D(p-w) + D(p+w))/((p+w)(p-w))
= 2Dp/(p^2 - w^2)

avg speed = total distance over total time
= 2D / (2Dp/(p^2 - w^2) )
= 2D ( p^2 - w^2)/(2Dp)
= (p^2 - w^2)/p

Answer 2

for a 1-km round trip, the time taken is
1/(p+w) + 1/(p-w) = 2/s
2p/(p^2-w^2) = 2/s
s = (p^2-w^2)/p