Thread: A challenging mechanics & application of calculus question?

From point A located on a highway as shown in attached figure, one has to get by car as soon as possible(in minimum time) to point B located in the field at a distance l from the highway. It is known that the car moves in the field η slower than on the highway. At what distance from point D one must turn off the highway?

It's an optimization problem, as far as I understand.

Let T be a point between C and D. And let |CT| = x. Assume that the car leaves the way from T. Now write the total time as a function of x. Then it's trivial to find it's minimum.

I was unable to write the function. Thats why I posted the problem. Anyone?

What is an optimization problem?