Actually I have spent quite a lot of time doing problem solving. If I can't think of an original problem, I try IOI or USACO tasks.
In that time you can explain that an algorithm is something that takes input, processes it and gives output. Nothing more. For example how long would it take to thoroughly complete and understand all the chapters of CLRS? And that's only the tip of the iceberg. A very small tip of it.
That's assuming you KNOW how to implement it. But algorithms can be very complex - there are problems only a few programmers are able to solve. It's not like reading a novel. It's not like "I have 30% of it figured out. I will figure the rest out tomorrow." Problem solving is trying to tackle the problem in different ways. Sometimes you will spend hours without any breakthroughs. It's science. It's art.The time it takes to understand and implement a particular algorithm -- 10 minutes to two weeks.
There's only one language to master - the programming logic, or pseudocode, whatever you call it. The rest is details.The time it takes to learn a new language at a basic level -- days to weeks.
The time it takes to learn something resembling a level of expertise or mastery with a language -- months and years.
If I can choose between a book about a programming language or a book about algorithms, data structures et cetera, I choose the latter. That's why I've never bought a book about a programming language.