At 1 PM, ship A is 5 kilometers strictly to the west of ship B. Ship A is sailing west at speed 20 km/hour and ship B is sailing north at 30 km/hour. Distance between ships changing at 3 PM?

Question

Here's the full question. PLEASE help asap. At 1 PM, ship A is 5 kilometres strictly to the west of ship B. Ship A is sailing west at speed 20 km/hour and ship B is sailing north at 30 km/hour. How fast (in km/hour) is the distance between ships changing at 3 PM?

Answer 1

1 pm ship A is 5 km west of ship B

ship A is traveling west at 20 km/hr

ship B is traveling north at 30 km/hr

how is the distance between them changing at 3pm?

it helps to draw a rough sketch

in 2 hours A is 45 miles west of B's original location

in 2 hours B is 60 miles north of B's original location

contruct a right triangle with legs 45 and 60, calculate the hypotenuse= sqr(45^2+60^2)=75 km

h^2 = n^2 + w^2

take the derivative

2hh' = 2nn' + 2ww'

divide by 2

hh' = nn' +ww'

75h' = 60(30)+45(20)

h' = (1800+900)/75

h'= 2700/75 = 108/3= 36 km/hr = rate of change of distance between the two ships