Question

a plane flies 420 miles with the wind and 320 miles against the wind at the same height . if the speed of the wind is 23 miles per hours, what is the speed of the plane in still air?

Answer 1

Answer :

Given :A plane flies 420 miles with the wind and 320 miles against the wind at the same height .

Here is no information regarding time taken we assume time taken by plane to cover these distance is same .

And

Speed of wind = 23 mile /hour

Let speed of plane in still air = x , So

Speed of plane with the wind = x + 23 mile / hour

And

Speed of plane against the wind = x - 23 mile / hour

we know

Time = $\frac{Dis\tan ce}{Speed}$ , So
$$\begin{gathered} \frac{420}{x+23}=\frac{320}{x-23} \\ \Rightarrow 420\left(x-23\right)=320\left(x+23\right) \\ \Rightarrow 420x-420\times 23=320x+320\times 23 \\ \Rightarrow 420x-320x=320\times 23+420\times 23 \\ \Rightarrow 100x=23\left(320+420\right) \\ \Rightarrow 100x=23\times 740 \\ \Rightarrow 100x=17020 \\ \Rightarrow x=\frac{17020}{100} \\ \Rightarrow \mathit{x}\mathbf{=}\mathbf{170}\mathbf{.}\mathbf{20} \end{gathered}$$
So,
Speed of plane in still air = 170.20 Mile / hour ( Ans )