From point A to point B, the distance between which is 60 km, a motorist and a cyclist left at the same time

From point A to point B, the distance between which is 60 km, a motorist and a cyclist left at the same time. It is known that a motorist drives 110 km per hour. more than a cyclist. Determine the speed of the cyclist if it is known that he arrived at point B 5.5 hours later than the motorist.

Let x be the speed of the cyclist, then the speed of the motorist will be (x + 110).

Let us express the cyclist’s travel time: 60 / h.

Let us express the time of the motorist on the way: 60 / (x + 110).

The cyclist was on the road 5.5 hours longer, let’s make the equation: 60 / x – 60 / (x + 110) = 5.5.

Let’s simplify the equation (divide by 5):

12 / x – 12 / (x + 110) = 1.1.

(12x + 1320 – 12x) / x (x + 110) = 1.1;

1320 / (x² + 110x) = 11/10;

11 (x² + 110x) = 13200;

11x² + 1210x – 13200 = 0;

x² + 110x – 1200 = 0.

D = 12100 + 4800 = 16900 (√D = 130);

x1 = (-110 – 130) / 2 = -120 (not suitable).

x2 = (-110 + 130) / 2 = 2- / 2 = 10 (km / h).

Answer: the speed of the cyclist is 10 km / h.