Close to idiot

A friend of mine teaches physics at a college. He told me many stories about how students these days lack abilities of thinking and application.
When he was explaining, in his physics class, a falling object on a slope using trigs (that's sin, cos, tan stuff), this student raised his hand and asked
"Is this sine the same one as we use in the mathematics?"
"Yes, of course."
"Then why didn't you tell us so first?"
The student for sure had learned trigs in the math class but in his mind, that's that. He'd had no prospect of applying it in his future despite that he is majoring in a field of science. If he encounters trigs somewhere, he never ever dreams that it is the same one he already learned.
What a tragedy! This is an alarming and deplorable phenomenon actually happening in Japan. It is also an evidence how Japanese students fail to acquire the habit of thinking.
When my friend ask a question
"How far do you go if you drive a car for 2 hours at a speed of 60 kilometers per hour?"
"120 kilometers."
They can answer easily. But when he changes the question to
"How many hours does it take to drive to a place 250 kilometers away at a speed of 60 kilometers per hour?"
Many students start to wonder if they should multiply or divide between two figures. It happens. according to his presumption, because students just memorized a formula,
d (distance) = v (velocity) * t (time)
The first question is all about the formula itself. Then they can answer. But the second one... First, you have to modify the formula. Second, they begin to get confused about what the variables (d, v, and t) stand for, like "was v for distance or speed?". And finally in this question 250 is not dividable by 60, which confuses them all the more. They always blindly believe that the answer must be dividable if they need to use division in answering.
This level is very close to idiot. Is there any good way to encourage them to think or to get the habit of applying what they learn? My friend voluntarily opened supplementary class for free (both for himself and for the students) after his regular class is over, and teach students one to one. The students who volunteer to come to the class are getting better in understanding what formulas mean and becoming able to apply them to questions. Good teachers are really needed. It might be one of the solutions.