Question

a cyclist moving 9 km/hr in still wind goes 16 km in the direction of wind amd comes back against the wind in total of 4 hours . determine the speed of wind.

Answer 1

Let the speed of the cyclist in the direction of the wind be (9 + v) km/hr, where v is the speed of the wind. So, the speed of the cyclist against the wind will be (9-v) km/hr.
The cyclist travels 16 km in the direction of wind and 16 km against the direction of wind while coming back.
So, time taken while going  = $\frac{16}{9+v}$ hrs
And time taken while coming back = $\frac{16}{9-v}$ hrs

So, total time of the journey is $\frac{16}{9+v} + \frac{16}{9-v}$ hrs
Which is given to be 4 hrs.

So, $\frac{16}{9+v} + \frac{16}{9-v} = 4$

Taking LCM-
$\frac{16(9-v)+16(9+v)}{(9+v)(9-v)} =  4$

=> $\frac{288)}{(81-v^{2})} = 4$

=> $\frac{288)}{4} = (81-v^{2})$
=> $72 = (81-v^{2})$
=> $v^{2} = 81 -72 = 9$

=> V = 3

Speed of wind is 3 km/hr