Question

an airplane travels 4688 kilometers against the wind in 8 hours and 5808 kilometers with the wind in the same amount of time. what is the rate of the plane in still air and what is the rate of wind

Answer 1

The speed of wind is 656 kmph and speed of plane is 70 kmph.

SOLUTION:

Given that, an air-plane travels 4688 kilometers against the wind in 8 hours

And 5808 kilometers with the wind in the same amount of time.  

We have to find the rate of the plane in still air and the rate of wind

Now, let the speed of wind be a kmph and speed of plane be b kmph.

And we know that, $\text { distance }=\text { speed } \times \text { time }$

$\begin{array}{l}{\text { Then, while travelling with wind } \rightarrow 5808=(a+b) \times 8 \rightarrow a+b=726 \rightarrow a=726-b \rightarrow(1)} \\\\ {\text { While travelling against wind } \rightarrow 4688=(a-b) \times 8 \rightarrow a-b=586 \rightarrow(2)}\end{array}$

Substituting (1) in (2) we get,

$\Rightarrow 726-b-b = 586\Rightarrow -2b=586-726 \Rightarrow -2b=-140$

$\Rightarrow b=\frac{140}{2} \Rightarrowb=70\Rightarrow (3)$

On substituting (3) in (1) we get,

$a=726-70=656\Rightarrow a=656$

Hence, the speed of wind is 656 kmph and speed of plane is 70 kmph.