The movements of two cyclists are given by the equations: x₁ = 8t, x₂ = 200-5t.

The movements of two cyclists are given by the equations: x₁ = 8t, x₂ = 200-5t. After 30 seconds, the distance between the cyclists will be equal to ..

x₁ (t) = 8 * t.

x₂ (t) = 200 – 5 * t.

t = 30 s.

S -?

Since cyclists move in the direction of the x axis, the distance S between them will be determined by the difference between the larger coordinate and the smaller one .: S = x₁- x₂.

Let’s find the coordinate of the first body after a time interval t = 30 s.

x₁ (30 s) = 8 * 30 = 240 m.

Let’s find the coordinate of the second body after a time interval t = 30 s.

x₂ (30 s) = 200 – 5 * 30 = 150 m.

Since the coordinate of the first body x₁ is greater than the coordinate of the second x₂, then: S = x₁- x₂.

S = 240 m – 150 m = 90 m.

Answer: after a time t = 30 s, the distance between the cyclists will be S = 90 m.