Ship A is traveling west at 40kkm/h and ship B is traveling north at 30mk/h. Both are headed for the Los Angeles Harbor.

Question

(a) At what rate are the boats approaching each other when ship A is 3km and ship B is 4km from the dock?

(b) At what rate would the distance between the boats be increasing if they started at the dock with the same speeds and after ship A has gone 5km and ship B has gone 12km?

Thanks in advance for the help!!

Answer 1

(a) at the moment specified, A and B are 5km apart

If ship A is a km from port and
ship B is b km from port,
the distance between them is given by

d^2 = a^2 + b^2
2d dd/dt = 2a da/dt + 2b db/dt
2(5) dd/dt = 2(3)(-40) + 2(4)(-30)
10 dd/dt = -240 + -240
dd/dt = -48

(b) Same formula, only now distances are increasing.
distance at time given is 13
2(13)dd/dt = 2(5)(40) + 2(12)(30)
26 dd/dt = 400 + 480
dd/dt = 33.8