Expert: Paul Klarreich - 10/20/2011

Question
At noon, ship A is 20 nautical miles due west of ship B. ship A is sailing west at 16 Knots and ship B is sailing north at 20 Knots. How fast is the distance between the ships changing at 5 PM

Answer
Questioner:leah
Country:Iowa, United States
Category:Calculus
Private:No
Subject:related rates
Question:
At noon, ship A is 20 nautical miles due west of ship B. ship A is sailing west at 16 Knots and ship B is sailing north at 20 Knots. How fast is the distance between the ships changing at 5 PM
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I assume you have seen:
http://en.allexperts.com/q/Calculus-2063/2009/11/Related-Rates-87.htm

So: Assuming the ORIGIN is B's position at noon:

Variables:
x = distance from A to Origin at time t.
y = distance from A to Origin at time t.
z = distance between A and B.

Rates:
dx/dt = 16
dy/dt = 20
dz/dt TO BE FOUND.

Relations:

x^2 + y^2 = z^2

AND at 5:00,  x = 100 (= 5*16 plus 20)
and at 5:00,  y = 100 (= 5*20)
and at 5:00,  z = 100 sqrt(2)

Differentiate:

2x dx/dt + 2y dy/dt = 2z dz/dt

You can finish now.