Question

An aeroplane made a trip of 1600 km against a head wind in 6 hours 20 min. It returned with the wind in 4 hours. Find its speed in still air and the veocity aof the wind

Answer 1

As speed = distance / time 
The total speed of the plane against the head wind = 1600 x 1000 / 22800
As speed = m /s .So the total speed against the wind is 70 km / h approximately.
The total speed of the plane during the return trip  = 1600 x 1000 / 14400
So the total speed in the direction of the wind is 111 km /h approximately . 
Now let the speed of the plane be x and the wind be y .
So the speed against wind is x - y = 70 km / h - equation 1
The speed in the direction of the wind is x + y = 111 km /h - equation 2
x = 70 + y from equation 1
Substitute x = 70 + y in equation 2
70 + y + y = 111 km /h 
70 + 2y = 111 
y = 111-70 / 2
y = 20.5 
Substitute y = 20.5 in equation 2 
x + 20.5 = 111
x = 111 - 20.5 
x= 90.5
Hence the speed of the plane in still air is 90.5 km/h and the velocity of the wind is 20.5 km/h.