I can give a very pictorial answer that doesn't require the use of actual pictures nor typesetting and might useful for beginners.
It is all about the misconception, encountered even in chemists with a relative experience in successful experiments, that solubility of the compounds in a mixture is a key factor for their effective chromatographic separation in thin films or columns.
Think of a large number of boats coming down a river just because of the water stream. Each boat has a boater aboard. This ensemble of boat/ers is the eluant.
Think of a number of berths and piers all along the banks. This is the stationary phase, the silica gel on plate in your example.
Now, you decide, or better someone wants you to do so, to go down the river as well. In order to use a boat, first of all the boat must no sink. This is an allegory for you being a molecule soluble in the eluant. If this prerequisite isn't met, you cannot even start your journey.
Say you find a boater that is friendly and the boat carries you, you start descend. However after some time you might find the trip tiring or boring, perhaps the boater is not the best companion you might think of. So you decide to take a break and jump out of the boat at the first next free pier. You might well stay there and relax until another boat with a friendly boater accept you so you restart the trip.
The scenario is repeated until you arrive at the mouth of the river.
Now imagine myself having to do the same. Obviously some of the boaters with not sinking boats must accept me as well. However, we are different persons, and what you find a friendly boater might be unpleasant to me, and viceversa. Similarly, I can be more or less at comfort than you, while sitting on a pier, so I do my best to leave it watching for a friendly boater.
Also, we can be oblige to stay aboard longer between two stops, because the pier can be occupied by one of the descending boats we are using, the boaters stop, too.
Assuming our taste and behaviour is at least a bit different (at the end we are different compounds, so it is) even if we start the descent together we'll arrive at the river's mouth separately at different time.
Note that the reason for this delay is not in the fact that the boat we used weren't sinking, i.e. our solubility, but in the number of boaters we were happy to cruise with and the level of comfort we found on free piers.
In other words, the delay is not due to time that we have spent on the boats - which is identical and depends on the river length and stream velocity - but on the time we stayed stationary at the little harbours all along.
The separation between our arrival times
depends ultimately on our relative affinity towards the boat/ers and the berthing places, i.e. the repartition we have between the liquid eluant and the stationary phase;
it is shortened more often/longer the boats stop, i.e. by an increase in affinity between the eluant and the stationary phase.
Changing the eluant composition equal to change the number of friendly boaters and free piers. The trick is to find boaters that are very friendly, say, to you, while minimizing those friendly to me. Still I need some, if I have to arrive as well.
To complete the answer, is it true that similar goes with similar and thus, a compound is likely more soluble in a solvent for which it has affinity. This equals to say that all the boats that don't sink necessarily have a boater which is at least moderately friendly.
As with human beings character and behaviour, it is complicated to find rules in details. If the mixture to be separated consists of very different compounds then the eluant choice is straightforward, otherwise one must start from the basic rules and proceed by feeling and experience.
Mixing different solvents allows to prepare eluants of different polarities in chromatographic sense, as I tried to convey with the above allegory. Other than general polarity (in terms of electric dipole moment), specific shape related issues or the presence of particular functional groups play a role, and this is indeed similar to the situation found when describing solubility, which cannot be reduced to a polar non-polar drastic criterion.
What I want to stress by this already long answer is that even a polar eluent can push unpolar compounds fast down the column (up the plate) by occupying the stationary phase. The unpolar compounds are forced to stay in the mobile phase in spite of their barely minimal solubility. They aren't separated exactly because they stay in solution. Chromatography is not a fractional crystallisation technique and passes huge amount of solvents over the sample, at the end.
In your case using just dichlorometane would have pushed the two faster togheter, using just hexane would have taken months, and for intermediate case you have done one to interpolate about.