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: $-10.12\,km/h$

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I have likely made a mistake somewhere.

Could someone help me determine which answer is correct?

  • 1
    $\begingroup$ Your solution is clearly laid out, and correct. $\endgroup$ Commented Jun 18, 2015 at 20:24
  • $\begingroup$ Do you agree with my result Peter? $\endgroup$
    – bru1987
    Commented Jun 18, 2015 at 20:38
  • $\begingroup$ @Peter do you agree with the result also? $\endgroup$
    – bru1987
    Commented Jun 18, 2015 at 20:45
  • $\begingroup$ I tried the alternative calculation (calculate the difference and derive at $x=\frac{1}{2}$) and approved your result. $\endgroup$
    – Peter
    Commented Jun 18, 2015 at 21:09
  • $\begingroup$ Does your textbook only give the answer? I would count more on those with fuller explanations and less problems. $\endgroup$
    – Kbot
    Commented Jun 18, 2015 at 21:51


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