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. Â
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, [tex]\text { distance }=\text { speed } \times \text { time }[/tex]
[tex]\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}[/tex]
Substituting (1) in (2) we get,
[tex]\Rightarrow 726-b-b = 586\Rightarrow -2b=586-726 \Rightarrow -2b=-140[/tex]
[tex]\Rightarrow b=\frac{140}{2} \Rightarrowb=70\Rightarrow (3)[/tex]
On substituting (3) in (1) we get,
[tex]a=726-70=656\Rightarrow a=656[/tex]
Hence, the speed of wind is 656 kmph and speed of plane is 70 kmph.
