Two cyclists set off on the 180-kilometer race at the same time. The first was driving 2 km / h

Two cyclists set off on the 180-kilometer race at the same time. The first was driving 2 km / h faster than the second, and arrived at the finish line 3 hours earlier. Find the speed of the cyclist who came to the finish line second.

Let the speed of the second cyclist be x km / h, and the first (x + 2) km / h.
We draw up an equation using the time formula t = S / V.
(180 / x) – (180 / (x + 2)) = 3;
Find the common denominator for the rational fractions on the left.
(180x + 360 – 180x) / (x (x + 2)) = 3;
360 / (x (x + 2)) = 3;
We multiply the left and right sides by the expression x (x + 2) in order to get rid of the denominator.
360 = 3 * x (x + 2);
360 = 3x ^ 2 + 6x;
We transfer all the term to the left, changing the signs to the opposite.
– 3x ^ 2 – 6x + 360 = 0;
3x ^ 2 + 6x – 360 = 0;
x ^ 2 + 2x – 120 = 0;
Find roots by Vieta’s theorem.
x1 = – 12; x2 = 10;
Speed ​​of the first cyclist x + 2 = 10 + 2 = 12 (km / h).
Speed ​​of the second cyclist x = 10 (km / h).
Answer: 12 km / h, 10 km / h.