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?
Question
Answer:
The speed of the wind is 25 km/hr.
Explanation:
Let us call [tex]v_p[/tex] the speed of the plane and [tex]v_w[/tex] 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). [tex]v_p – v_w = \dfrac{900km}{120min}[/tex]
And when the plane is flying with the wind, it covers the same distance in 1 hour 48 minutes (108 minutes)
(2). [tex]v_p+v_w= \dfrac{900km}{108min}[/tex]
From equation (1) we solve for [tex]v_p[/tex] and get:
[tex]v_p = \dfrac{900km}{120min}+v_w[/tex],
and by putting this into equation (2) we get:
[tex]\dfrac{900km}{120min}+v_w+v_w= \dfrac{900km}{108min}[/tex]
[tex]2v_w= \dfrac{900km}{108min}-\dfrac{900km}{120min}[/tex]
[tex]2v_w = 8.3km/min – 7.5km/min[/tex]
[tex]2v_w = 0.83km/min[/tex]
[tex]v_w = 0.4165km/min[/tex]
or in km/hr this is
[tex]\boxed{v_w= 25km/hr }[/tex]