Originally Posted by

**Phire** Right, I should've said speed. I believe the problem presents a distance as a function of time, which I think results in a derivative of velocity, however I'm not sure if that actually applies to this problem. The problem asks how fast the distance changes between them 4 hours later, but both of the boats are traveling at a constant speed, therefore I would guess that the rate is always 60 km/hr, but what the book did is this:

$\displaystyle d = \sqrt{100^2 + (25t + 35t)^2}$

(d as in distance)

It uses the distance formula.

The derivative comes out to:

$\displaystyle \frac{dd}{dt} = 3600t(10000+3600t^2)^{-1/2}$

4 hours later, the distance changes at 55 km/s, but like I said above, if the boats are traveling at a constant speed, why would there be a difference at any moment of time?