# 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 $a$ 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?
Code:
                          * B
* |
*   | 5t
*     |
P * - - - - - * - - - * Q
|         *         :
|       *           :
35t |     *             : 35t
|   *               :
| *                 :
A * - - - - - - - - - * R
100

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

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

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

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

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

Can you finish it now?

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