A man is cycling in a place where wind is blowing. He travels 12 km against the direction of the blowing wind. In doing so, he took the same time while going 28 km in the direction of the wind. Find the speed of the wind. ( Hint - When the man is cycling in the direction of the wind, wind speed is added to his speed; otherwise it is subtracted.)

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.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1