Question

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

Well, you first need to find a formula for how far apart they are. Using the pythagorean theorem, \(d=\sqrt{(40+15t)^2+(17t)^2}\). We have the \(40+15t\) since ship A starts 40 miles west, and then sails further west at 15 knots. Similarly, we have \(17t\) since ship B starts 0 miles north, and travels north at 17 knots. This make sense?