special relativity - Why don't clocks on a train read the same time?

Two clocks are positioned at the ends of a train of length $L$ (as measured in its own frame). They are synchronized in the train frame.

The train travels past you at speed $v$. It turns out that if you observe the clocks at simultaneous times in your frame, you will see the rear clock showing a higher reading than the front clock. By how much?

The solution to this exercise is given in the book, and it denotes that we put "a light source on the train, but let’s now position it so that the light hits the clocks at the ends of the train at the same time in our frame." As in this figure:

I don't understand:

1. Why is there a difference in the clocks in the first place?


2. Why are the fractions are multiplied by half? i.e. what is the origin of the $2$ in $$\frac{L(c+v)}{\textbf{2}c}\text{?}$$

Note: This one is taken from David Morin textbook for mechanics.