A cyclist is riding down the Saint Marks trail. On the way day, he rides into a headwind at a piece of 24.2 mph. On the trip back, he rides with a tailwind a piece of 26.1 mph. What is the speed of a cyclist in the wind?

The speed of the cyclist is 25.15 mph and that of the wind is 0.95 mph.

Step-by-step explanation:

When the wind is opposite to the motion of the cyclist then his speed is 24.2 mph and when the wind is in the direction of motion of the cyclist then his speed is 26.1 mph.

So, if the speed of the cyclist is u mph and the speed of the wind is v mph, then we can write

u + v = 26.1 ... (1)

And, u - v = 24.2 ... (2)

Now add those two equations we get 2u = 50.3

⇒ u = 25.15 mph

And from equation (1) we get, v = 26.1 - 25.15 = 0.95 mph

Hence, the speed of the cyclist is 25.15 mph and that of the wind is 0.95 mph. (Answer)