Ship A is 15 miles east of point O and moving west at 20mi/h. Ship B is 60 miles south of O and moving north at 15mi/h. a)Are they approaching or seperating after 1 hour and at what rate? b)after 3hrs?

Let D=distance between the ships at time t

$\displaystyle D^2=(60-15t)^2+(15-20t)^2$

$\displaystyle 2D*\frac{dx}{dt}=(2)(-15)(60-15t)+(2)(-20)(15-20t)$

$\displaystyle 2D*\frac{dx}{dt}=(-30)(60-15t)+(-40)(15-20t)$

$\displaystyle 2D*\frac{dx}{dt}= 1250t-2400 $

$\displaystyle \frac{dx}{dt}=\frac{1250t-2400}{2D}$

$\displaystyle D=\sqrt{5^2+45^2}=5\sqrt{82}$

$\displaystyle \frac{dx}{dt}=\frac{1250t-2400}{10\sqrt{82}}$

a)$\displaystyle \frac{dx}{dt}=\frac{1250*1-2400}{10\sqrt{82}}=approaching\ at \frac{-115}{\sqrt{82}}$ mi/h

b)$\displaystyle \frac{dx}{dt}=\frac{1250*3-2400}{10\sqrt{82}}=seperating\ at \frac{135}{\sqrt{82}}$ mi/h

The book agrees with me on part A, but on part B it says the answer should be $\displaystyle seperating\ at\ \frac{9\sqrt{10}}{2}$ mi/h. Am I missing something obvious or is the book wrong here?