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

Let the speed of plane in still air be x km/h

Speed of wind = 30 km/h

∴ Speed of plane in wind = (x + 30) km/h and Speed of plane against wind = (x - 30) km/h.

40 minutes = $\dfrac{40}{60} \text{ hours } = \dfrac{2}{3} \text{ hours }$

According to question,

$\Rightarrow \dfrac{3600}{x - 30} - \dfrac{3600}{x + 30} = \dfrac{2}{3} \\[1em] \Rightarrow \dfrac{3600(x + 30) - 3600(x - 30)}{(x - 30)(x + 30)} = \dfrac{2}{3} \\[1em] \Rightarrow \dfrac{3600x + 108000 - 3600x + 108000}{x^2 - 30x + 30x - 900} = \dfrac{2}{3} \\[1em] \Rightarrow 216000 \times 3 = 2(x^2 - 900) \text{ (On cross multiplying) }\\[1em] \Rightarrow 648000 = 2(x^2 - 900) \\[1em] \Rightarrow 324000 = x^2 - 900 \text{ (Dividing the complete equation by 2) } \\[1em] \Rightarrow x^2 - 900 - 324000 = 0 \\[1em] \Rightarrow x^2 - 324900 = 0 \\[1em] \Rightarrow x^2 - (570)^2 = 0 \\[1em] \Rightarrow (x - 570)(x + 570) = 0 \\[1em] \Rightarrow x - 570 = 0 \text{ or } x + 570 = 0 \\[1em] x = 570 \text{ or } x = -570 \\[1em]$

Since speed of aeroplane cannot be negative hence, x ≠ -570.

The speed of aeroplane in still air is 570 km/h.