# Thread: ships and related rates

1. ## ships and related rates

At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 5 km/h. How fast is the distance between the ships changing at 6:00 PM?

I understand how to do these types of problems, but for this one I can't figure out the right equation to differentiate. Anybody want to point me in the right direction?

Thanks for the help

2. Hello, Climberboy123!

At noon, ship $\displaystyle a$ is 100 km west of ship $\displaystyle b$.
Ship $\displaystyle a$ is sailing south at 35 km/h and ship $\displaystyle b$ is sailing north at 5 km/h.
How fast is the distance between the ships changing at 6:00 PM?
Code:
                          * B
* |
*   | 5t
*     |
P * - - - - - * - - - * Q
|         *         :
|       *           :
35t |     *             : 35t
|   *               :
| *                 :
A * - - - - - - - - - * R
100

Ship $\displaystyle a$ starts at $\displaystyle P$ and sails south at 35 km/hr,
. . In $\displaystyle t$ hours, it has sailed $\displaystyle 35t$ km to point $\displaystyle A.$

Ship $\displaystyle b$ starts at $\displaystyle Q$ and sails north at 5 km/hr.
. . In $\displaystyle t$ hours, its has sailed $\displaystyle 5t$ km to point $\displaystyle B.$

Note that: .$\displaystyle PQ = AR = 100$ km.

Let: $\displaystyle x \,=\,AB.$

In right triangle $\displaystyle BRA\!:\;\;x^2 \;=\;(40t)^2 + 100^2 \quad\Rightarrow\quad x \;=\;(1600t^2 + 10,\!000)^{\frac{1}{2}}$

Can you finish it now?

3. thanks! I should be able to get it now.