Hello, hsidhu!

The first one is tricky to set up . . .

1. A toy tugboat is launched from the side of a pond and travels north at 5 cm/s.

At the same moment, a toy launch starts from a point *meters* northeast

of the tugboat and travels west at 7 cm/s.

How closely do the two tugboats approach each other?

Answer: 186 cm Code:

800-7t L 7t
B o - - - o - - - - - - - o C
| / * |
| / * |
| / d * |
800-5t| / _ * |
| / 800√2 * |
| / * | 800
|/ * |
T o * |
| * |
5t | * |
| * 45° |
A o - - - - - - - - - - - o D
800

The tugboat starts at and goes north at 5 cm/sec.

In seconds, it travels cm to

The launch starts at and goes west at 7 cm/sec.

In seconds, it travels cm to

Since , it is the diagonal of an 800-cm square

. .

Hence: .

We want to minimize distance: .

In right triangle

Let

We have: .

. . and that is the function we must minimize.

*Go for it!*

Edit: E.B. beat me to it . . . *sigh*

.