Question

A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with the wind covers the same distance in 1 hour and 48 minutes. If the speed of the wind is constant, what is the speed of the wind?

Answer 1

Answer:

The speed of the wind is 25 km/hr.

Explanation:

Let us call $v_p$ the speed of the plane and $v_w$ the speed of the wind. When the plane is flying against the wind, it covers the distance of 900-km in 2 hours (120 minutes); therefore;

(1). $v_p - v_w = \dfrac{900km}{120min}$

And when the plane is flying with the wind, it covers the same distance in 1 hour 48 minutes (108 minutes)

(2). $v_p+v_w= \dfrac{900km}{108min}$

From equation (1) we solve for $v_p$ and get:

$v_p = \dfrac{900km}{120min}+v_w$,

and by putting this into equation (2) we get:

$\dfrac{900km}{120min}+v_w+v_w= \dfrac{900km}{108min}$

$2v_w= \dfrac{900km}{108min}-\dfrac{900km}{120min}$

$2v_w = 8.3km/min - 7.5km/min$

$2v_w = 0.83km/min$

$v_w = 0.4165km/min$

or in km/hr this is

$\boxed{v_w= 25km/hr }$