# The circumference of the front wheel of a special bike is 0.6 m less than the circumference of the rear wheel.

The circumference of the front wheel of a special bike is 0.6 m less than the circumference of the rear wheel. At a distance of 36 m, the front wheel makes 5 revolutions more than the rear one. Find the circumference of each wheel.

Suppose that the circumference of the rear wheel is x meters, then the circumference of the front wheel is x – 0.6 meters.

At a distance of 36 meters, the rear wheel will make 36 / x revolutions, and the front, respectively, will make 36 / (x – 0.6) revolutions.

According to the condition of the problem, we compose the equation:

36 / (x – 0.6) = 36 / x + 5,

36 / (x – 0.6) = (36 + 5 * x) / x,

36 * x = 36 * x – 21.6 + 5 * x² – 3 * x,

5 * x² – 3 * x – 21.6 = 0.

Let’s find the discriminant of this equation:

D = (-3) ² – 4 * 5 * (-21.6) = 9 + 432 = 441.

Therefore, the equation has the following solutions:

x = (3 – 21) / 10 = – 1.8 and x = (3 + 21) / 10 = 2.4.

Since x can only be a positive number, the circumference of the second wheel is 2.4 meters, and the first, respectively, 2.4 – 0.6 = 1.8 meters.

Answer: 1.8 meters and 2.4 meters.

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