Question

An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.

Answer 1

Let the speed of the plane in still air = x km/hr
Speed of wind = 30km/hr
Distance = 3600km

∴ Time taken with the wind = `(3600)/(x + 30)`

and time taken against the wind = `(3600)/(x - 30)`
According to the condition,

`(3600)/(x - 30) - (3600)/(x + 30) = 40"mnutes" = (2)/(3)"hour"`

⇒ `3600((1)/(x - 30) - (1)/(x + 30)) = (2)/(3)`

⇒ `3600((x + 30 - x + 30)/((x - 30)(x + 30))) = (2)/(3)`

⇒ `(3600 xx 60)/(x^2 - 900) = (2)/(3)`

⇒ 2x² - 1800 = 3 x 3600 x 60
⇒ 2x² - 1800 = 648000
⇒ 2x² - 1800 - 648000 = 0
⇒ 2x² - 649800 = 0
⇒ x² - 324900 = 0  ..(Dividing by 2)
⇒ x² - (570)2 = 0
⇒ (x + 570)(x - 570) = 0
Either x + 570 = 0,
then x = -570
which is not possible as it is negative
or
x - 570 = 0,
then x = 570
Hence speed of plane in still air = 570km/hr.