A cyclist and a motorcyclist drove from one point to another. The speed of the motorcyclist is 10 km / h

A cyclist and a motorcyclist drove from one point to another. The speed of the motorcyclist is 10 km / h more than the speed of the cyclist, so he spent 6 hours less on the way. What is the speed of a motorcyclist?

The condition lacks a point about the fact that the whole way is 120 km.
First, let’s write down a short condition:
X km / h is the speed of the cyclist.
Based on the condition: (x + 10) km / h – the speed of the motorcyclist.
120 / h hour – the travel time of the cyclist.
120 / (x + 10) hour. – the travel time of the motorcyclist.
Following the condition, the difference in the elapsed time is 6 hours, hence the equality:
120 / x – 120 / (x + 10) = 6;
Let’s solve it:
120 (x + 10) – 120x = 6x (x + 10).
120x + 1200 – 120x = 6×2 + 60x.
6×2 + 60x – 1200 = 0.
x2 + 10x – 200 = 0.
Solving this quadratic equation, calculating the discriminant, we find: x = 10 km / h – this is the speed of the cyclist.
And by condition: x + 10 = 10 + 10 = 20 (km / h) – the speed of the motorcyclist.
Answer: the speed of the cyclist is 10 km / h, the speed of the motorcyclist is 20 km / h.