Issues with text problems

One idea is cognitive load. The student knows enough to establish any particular piece of the problem, but has trouble juggling everything when there are too many components. I think word problems have a higher cognitive load than drill problems because the reader has to read through the whole thing and keep several ideas in their head at once before beginning to synthesize a response. This is related to math anxiety where in a sense a student's own negative perceptions about math and their ability to do it start to drain cognitive energy. I agree with Krishnakanth that this problem has been exacerbated by the educational system in some places, which teaches math as a list of recipes to follow and doesn't emphasize the analytical, critical thinking aspects.

For this particular case: We may understand that the definition of a 10% slope is mathematically obvious.

But, by couching it in these natural English language terms, it could give the impression to students that they require outside knowledge (whether or not they actually do need outside knowledge).

Students may be aware that "10% slope" has a particular meaning in English, having seen it on road signs, but probably have not directly associated that to a mathematical meaning. This could be one source of their confusion. When I see 10% used in natural English, I wouldn't immediately think about how that converts to a decimal, say.

More generally: Plenty of words have a slightly different meaning in natural English and mathematical language - including 'slope' itself. Students frequently (and correctly) understand that they have to handle their use mathematical language in a very careful way. By phrasing a question using natural language, this link with precision might be broken and confusing to students.

It may not be clear to students how to cross-interpret a question that is partly in mathematical language and partly in natural English. It doesn't help that questions written in natural language are sometimes badly phrased! Students might have developed a fear of these questions because their understanding of the reality of the situation doesn't match their own internal mathematical knowledge.

Indeed, there may be a disassociation between mathematical questions and actual reality. Question setters tend to insert mathematics into 'real' situations where they don't belong (or don't apply exactly correctly). In reality, as I understand, it would be unlikely and impractical to model a hill as a parabola. Apart from the apparent sign error, a hill is 3D and a slope can be overcome by tracking a zigzag ascent up diagonally. It is (perhaps) an unnatural and contrived question, phrased in natural language in a context which is unfamiliar to students. This could be a further source of confusion.

I think that interpreting (and writing) natural language questions is a difficult skill that has to be learned (and taught). I think all mathematicians come across situations where they have suddenly realised how a particular skill can be used in an unfamiliar or surprising situation - it's clear that this might happen more often to novice students.

To answer your question:

I think you could help students by teaching this specifically:

When I solve such problems I start with "What do I know?", then "What does that mean in mathematical definitions?"

Interpreting an English statement is not straightforward, and students would benefit from learning how to do this. Explaining how you do this, yourself, is a good idea!

This is a very interesting question. On the one hand, we're told that we need to make maths more interesting by relating it to real life as in your sample question, but on the other, doing so creates the heavy cognitive load that Jim Conant refers to. To try to answer the question rather than just discuss this topic, these guys suggest that showing worked examples can lessen the load and help students to learn how to solve similar problems. And since problem solving is mentioned, there's Polya or John Mason. (I forget the source now and can't track it down, but I recall reading a quote by a teacher of problem solving that his approach was to give his students problems and not tell them the answer!)