How do I account for differences in time in a time-speed-distance problem?

Question

I'm sorry if the language is a bit hard to read I am not an English speaker so everything is translated.

I have this question "A train rides every day in a constant speed from A to B. The distance between A to B is 120km. One day, the train had an unexpected stop at the midpoint between A to B (which I will from now refer to as M) for 10 minutes. For the train to get to point B on time (as in, not late 10 minutes), the train has to increase it's speed by 12km/h. Find the speed at which the train normally goes at"

from what I understand, it hours 60km for 60/x time (where x is the speed at which it normally goes at) for the first half and for the second half for 60/(x+12) hours, where is the 10 minutes inserted in this? I'm completely lost.

Answer 1

$$\frac{120}{x}=\frac{60}{x}+\frac{60}{x+12}+10$$

Answer 2

$$ \frac{120}{x}=\frac{60}{x}+\frac{60}{x+12}+\frac{1}{6} \Rightarrow x=60 \text{ km/h} $$ Note: 10 minutes is $\frac{1}{6}$ hours.