# Thread: Studying for final and need help with Related Rates

1. ## Studying for final and need help with Related Rates

I hate word problems and I pretty much suck when it comes to them. Here's one that I got stuck at.

1) A man starts walking north at 4ft/s from a point P. Five minutes later a woman starts walking south at 5ft/s from a point 500ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

I don't even know where to begin. My final will be filled with these types of question any tips on how to approach these types of problems?

2. Tip... draw out what is given in the problem. In related rates & optimization problems, you tend to work with one or two formulas and take a derivative of one of them.

3. Originally Posted by colby2152
Tip... draw out what is given in the problem. In related rates & optimization problems, you tend to work with one or two formulas and take a derivative of one of them.
I usually do that, and whenever I can list what x =, y=, and the rates of change, but sometimes I don't know what goes with what.

4. Hello, FalconPUNCH!

Make a sketch!

1) A man starts walking north at 4ft/s from a point P.
Five minutes later a woman starts walking south at 5ft/s from a point 500ft due east of P.
At what rate are the people moving apart 15 min after the woman starts walking?
Code:
    M *
| *
4t |   *
|     *
A *       *
|         *
|           *
1200 |             *
|               *
|                 *
P * - - - - - - - - - * - - - * Q
:                     *     |
5t :                       *   | 5t
:                         * |
R * - - - - - - - - - - - - - * W
500

The man starts at P and has a 5-minute headstart.
In 5 minutes (300 sec), he walks 1200 feet to point A.
In the next $\displaystyle t$ seconds, he walks $\displaystyle 4t$ ft to point M.

The woman starts at Q and walks south at 5 ft/s.
In the next $\displaystyle t$ seconds, she walks $\displaystyle 5t$ ft to point W.

Let $\displaystyle x \,=\,MW$
In right triangle MRW, we have: .$\displaystyle MW^2 \:=\:MR^2 + RW^2$
. . That is: .$\displaystyle x^2\:=\4t+1200 + 5t)^2 + 500^2 \:=\9t+1200)^2 + 500^2$

Differentiate with respect to time: .$\displaystyle 2x\left(\frac{dx}{dt}\right) \:=\:2(9t + 1200)$

. . Hence: .$\displaystyle \frac{dx}{dt} \;=\;\frac{9t + 1200}{x}$

In 15 minutes, $\displaystyle t = 900$
Find $\displaystyle x$ at that time, and you're done!

5. Originally Posted by Soroban
Hello, FalconPUNCH!

Make a sketch!

Code:
    M *
| *
4t |   *
|     *
A *       *
|         *
|           *
1200 |             *
|               *
|                 *
P * - - - - - - - - - * - - - * Q
:                     *     |
5t :                       *   | 5t
:                         * |
R * - - - - - - - - - - - - - * W
500

The man starts at P and has a 5-minute headstart.
In 5 minutes (300 sec), he walks 1200 feet to point A.
In the next $\displaystyle t$ seconds, he walks $\displaystyle 4t$ ft to point M.

The woman starts at Q and walks south at 5 ft/s.
In the next $\displaystyle t$ seconds, she walks $\displaystyle 5t$ ft to point W.

Let $\displaystyle x \,=\,MW$
In right triangle MRW, we have: .$\displaystyle MW^2 \:=\:MR^2 + RW^2$
. . That is: .$\displaystyle x^2\:=\4t+1200 + 5t)^2 + 500^2 \:=\9t+1200)^2 + 500^2$

Differentiate with respect to time: .$\displaystyle 2x\left(\frac{dx}{dt}\right) \:=\:2(9t + 1200)$

. . Hence: .$\displaystyle \frac{dx}{dt} \;=\;\frac{9t + 1200}{x}$

In 15 minutes, $\displaystyle t = 900$
Find $\displaystyle x$ at that time, and you're done!

LOL my sketch didn't look like that. But I understand what to do. Usually most have something to do with triangles, so I'm expecting my professor to do one with triangles. Thanks for helping me out with the example.