Asked by Mitzi

At 8:00am, ship A is 120km due east of ship B. Ship A is moving north at 20km/hr, and ship B is moving east at 25km/hr. How fast is the difference between the two ships changing at 8:30am?
Answered by Reiny
After t hours,
ship A has traveled 20 t km
ship B has traveled 25t

I sketched a right-angled triangle with
legs 120-25t and 20t
let D be the distance between them , making D the hypotenuse

D^2 = ((120- 25t)^2 + (20t)^2
at 8:30 , t = .5
D^2 = 11656.25
D = 107.964..

2D dD/dt = 2(120-25t)(-25) + 2(20t)(20)
so when t= .5 and D = 107.964..

dD/dt = ( (120-12.5)(-25) + 10(20) )/107.964
= -23.04..

so at 8:30 , the distance between them is decreasing at appr 23 km/h

check my calculations
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