Posted by **Parker** on Thursday, September 24, 2009 at 11:55pm.

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

- calculus -
**Reiny**, Friday, September 25, 2009 at 12:17am
let t hours be some time past 12:00 noon

After t hours, ship B has gone 20t knots

and ship A has gone 17t knots

let the distance between them be D

I see a right-angled triangle and

D^2 = (20t)^2 + (17t+10)^2

D^2 = 689t^2 + 340t + 100

2D(dD/dt) = 1378t + 340

dD/dt = (689t + 170)/D

at 4:00 pm, t=4 and

D^2 = 12484

D = 111.7318

so at t=4

dD/dt = (689(4) + 170)/111.7318

= 26.19 knots

- calculus -
**Parker**, Friday, September 25, 2009 at 1:56am
It still says NOT CORRECT.

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