To determine the wind speed, we can use the concept of relative velocity. Let's assume that the wind speed is represented by "W" km/hr.
When the plane is flying into the headwind, its effective ground speed is reduced by the wind speed. So, the ground speed during this leg of the journey is 300 km/hr - W km/hr.
During the return trip, the plane is flying with the wind, which adds to its ground speed. So, the ground speed during this leg of the journey is 300 km/hr + W km/hr.
We know that distance = speed × time, and since the distance covered is the same in both directions, we can set up the following equation:
(300 km/hr - W km/hr) × (48/60 hr) = (300 km/hr + W km/hr) × (42/60 hr)
Let's solve this equation to find the value of W (wind speed):
(300 - W) × (48/60) = (300 + W) × (42/60) (300 - W) × 48 = (300 + W) × 42 14400 - 48W = 12600 + 42W 90W = 1800 W = 1800 / 90 W = 20 km/hr
Therefore, the wind speed is 20 km/hr.