# Related Rates - possible textbook error

Recently I've been asked to do some exercises from a textbook but I cannot understand how the author derived the correct answer.

Here is the exercise in question:

At $8$:$00$ boat $A$ is located $25\,km$ south of boat $B$. If boat $A$ is traveling west at $16\,km/h$ and boat $B$ south at $20\,km/h$, at what rate is the distance between the boats changing at $8$:$30$?

Textbook answer: $25.6\,km/h$

My answer: $-10.12\,km/h$

I have likely made a mistake somewhere.

Could someone help me determine which answer is correct?

• Your solution is clearly laid out, and correct. Commented Jun 18, 2015 at 20:24
• Do you agree with my result Peter? Commented Jun 18, 2015 at 20:38
• @Peter do you agree with the result also? Commented Jun 18, 2015 at 20:45
• I tried the alternative calculation (calculate the difference and derive at $x=\frac{1}{2}$) and approved your result. Commented Jun 18, 2015 at 21:09
• Does your textbook only give the answer? I would count more on those with fuller explanations and less problems.
– Kbot
Commented Jun 18, 2015 at 21:51