Hello, ihmth!

There is a back-door approach to this problem,

. . involving optics and striaght-line paths.

But I'll use the expected Calculus set-up.

1) A ship lies 6 mi. from shore.

Opposite a point 10 mi. farther along the shore another ship lies 18 mi. offshore.

A boat from the first ship is to land a passenger and then proceed to the other ship.

What is the least distance the boat can travel? Code:

* C
* |
* |
* |
A * * |
| * * | 16
| * * |
6 | * * |
| * * |
| * * |
B * - - - - - * - - - - - - - - - * D
x P 10 - x

The first ship is

The second ship is at

And: .

Let be the landing point.

Then: .

In right triangle

In right triangle

The distance travelled is: .

. . and **that** is the function we must minimize.