Answer:
The speed of the wind is 4.8 km/hr
Step-by-step explanation:
The parameters of the motion of the man are;
The distance the man travels in the given time while moving against the wind = 12 km
The distance the man travels in the giving time while going with the wind = 28 km
From search online for of a similar question, we have;
The speed with which the man is cycling = 12 km/hr
Let. 't', represent the time the travels each distance, let 'w', represent the speed of the wind and let 'v' represent the speed of the man, we have;
Time, t = Distance, d/(Velocity, v)
The resultant speed of the man when he travels against the wing = v - w
The resultant speed of the man when he goes in the the wing = v + w
Therefore, we have;
12/(v - w) = 28/(v + w)
12·v + 12·w = 28·v - 28·w
12·w + 28·w = 28·v - 12·v = 16·v
40·w = 16·v
∴ w = (16/40) × v = (2/5) × v
The speed with which the man is cycling = 12 km/hr
∴ The speed of the wind, w = (2/5) × v = (2/5) × 12 km/hr = 4.8 km/hr
The speed of the wind = 4.8 km/hr.
