How fast is the distance between the ships changing at t = 3pm
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How fast is the distance between the ships changing at t = 3pm

[From: ] [author: ] [Date: 11-10-30] [Hit: ]
I just cant seem to get it.dz/dt = 675/85 = 7.94 km/hr-You are very welcome.Thanks & Regards.......
I'm having a lot of trouble with this question. I can't seem to get any of the below answers.

At noon, ship A is a distance d = 130km west of ship B.
Ship A is sailing east at a speed of v = 30km/h.
Ship B is sailing north at a speed of v = 25km/h.
How fast is the distance between the ships changing at t = 3pm?

I just can't seem to get it.

-
Edit: added some explanation for you:
let:
t = time => units in hours
x = distance traveled by ship A => units in km
y = distance traveled by ship B => units in km
z = the distance between the ships at 3 pm => units in km
dx/dt = 30 km/h
dy/dt = 25 km/h
find dz/dt at t = 3 hr

z^2 = (130 - x)^2 + y^2
2z dz/dt = 2(130 - x) (-dx/dt) + 2ydy/dt
at 3 pm:
x = 3* 30 = 90
y = 3 * 25 = 75
z =√[(130 - 90)^2 + 75^2] = 85
2z dz/dt = 2(130 - x) (-dx/dt) + 2ydy/dt
dz/dt = 1/85*[(130 - 90)(-30) + (75 * 25)]
dz/dt = 1/85*[-1200 + 1875]
dz/dt = 675/85 = 7.94 km/hr

-
You are very welcome.

Thanks & Regards.

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