***At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h a

Question

***At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM?*** I already tried this problem 3-4 times. The answer is NOT 17.4 km/hour, 37.6 km/hour, or 20.6 km/hour. I followed this example: "At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?" but I was able to find the answer for the example problem.

Explanation / Answer

drawing should be a right triangle with sides (150-x), y, and z so dx/dt=35 and dy/dt=25 set up the equation based on your drawing. z^2=(150-x)^2+y^2 take the derivative and get dz/dt= (1/z)((x-150)dx/dt+y dy/dt) to find x you take 4 (time elapsed since 12) and multiply it by 35 for x and 25 for y. So x = 140 and y = 100. For z, use the pythagorean theorem. z=sqrt(10^2+100^2) Plug everything back into the equation. dz/dt= ((140-150)(35)+100(25))/sqrt(10,100) dz/dt = 21.4 km/h

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