Any difference between 'quelque' and 'un peu de' when both mean 'a bit of'? Are they interchangeable?

Question

Il a quelque difficulté à se concentrer pour faire ses devoirsIl a un peu de difficulté à se concentrer pour faire ses devoirs

Accepted Answer

Hi Joan,
That's an interesting question and it did get me thinking...
Quelque in the singular means some in English, in other words, an indeterminate amount of something.
e.g.
Ils habitent à quelque distance de chez nous = They live some distance/way from our house
Il y a quelque temps que je ne l'ai pas vu = I have not seen him for some time 
so, in your example -
He has some difficulty in concentrating = Il a quelque difficulté à se concentrer
Quelques in the plural can mean some too but also a few - 
Il a quelques amis chez lui pour le weekend = He has to a few friends to stay at the weekend
Elle a réfléchi quelques instants avant de répondre = She pondered for a few instants before answering
J'ai quelques problèmes en ce moment = I have a few problems at the moment
'Un peu de' is more specific as it means, a small amount of -
un peu de = a small quantity  ( a bit of - a little )
e.g.
Je demande un peu de calme = I am asking for a bit of calm
Il a un peu de sinusite en ce moment = He has a touch of sinusitis at the moment
Hope this helps!

Answer

Il a quelques difficultés à se concentrer. -- He has some difficulties to concentrate. Il a un peu de difficulté à se concentrer. -- He has a bit of difficulty to concentrate.They come close in their meaning but still, there is some difference. I certainly have some difficulty in describing it in any meaningful way. Maybe you can get the difference by staring at the example sentences? The input of a native speaker would certainly be helpful, too.