Relative rates question

Question

Hello, could someone help me with this homework question?:

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4 pm?

Answer 1

Let x be the distance ship A travels east. The distance between A and B forms a right triangle with the hypotenuse, h, being the distance between the ships. Let y be the distance B travels north.

h² = (150-x)² +y²

Given dx/dt = 35 km/h and dy/dt = 25 km/h

Want to find dh/dt

Differentiating

2hdh/dt = 2(150-x)(-1)dx/dt +2ydx/dt

dh/dt = ((x-150)dx/dt +ydx/dt)/h

At 4:00 PM

x = 35•4 = 140

y = 25•4 = 100

h = √((150-140)²+100²) = √(100+100²) = 10√101

dh/dt = (-10(35) +100(25)/10√101

= (-350 + 2500)/10√101

= 2150/10√101 ≈ 21.39 km/h