At noon, ship A is 110 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

Question

anonymous · Answer

This is a related rates problem, right?

anonymous · Answer

Okay, let $x$ be the position for A, $y$ position for B and $z$ the distance between.

anonymous · Answer

We know from Pythagorean theorem $$
z^2=x^2+y^2
$$And using implicit differentiation:$$
2zz'=2xx'+2yy'
$$

anonymous · Answer

They also give us the velocities, in this case $x'=25$ and $y'=15$.

anonymous · Answer

We need to find $x$ and $y$.  Then use that to find $z$.

anonymous · Answer

But we can't ignore time either.  They gave us $x$ at noon, but we want $x$ at 4pm

anonymous · Answer

They also implicitly gave us $y$ at noon too (it's 0).

anonymous · Answer

@salimssa  What do you think?