Find distance in km/h

Question

At noon ship A is sailing south at 35 km/hr and ship B is sailing east at 25 km/hr. How fast is the distance between the ships changing at 4:00?

Answer 1

Assuming both ships start from the same location, this forms a right triangle.

Given:

dA/dt = 35 km/hr

dB/dt = 25 km/hr

Let s be the distance between the two ships.

Need to find ds/dt

At 4:00 ship A has traveled 140 km south and ship B has traveled 100 km east.

s² = A²+B²

2sds/dt = 2AdA/dt+2BdB/dt

ds/dt = (AdA/dt + BdB/dt)/s

The distance between the two ships is:

s = √(140²+100²) = 172.05

ds/dt = (140(35)+100(25))/172.05 ≈ 43 km/hr