A male starts walking north at 3 ft/s from a point P. Five minutes later on a womale starts walking south at 4 ft/s from a point 500 ft due east of P. At what price (in ft/s) are the world moving apart 15 minutes after the woman starts walking? (Round your answer to two decimal locations.)

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Let t be the moment in minutes after the womale starts walking.

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Then if we say the beginning (0,0) is at P

At time t

The man is at (0, 3 (5+t))

The womale is at (-4t, -500)

If s is distance in between them, then s2 = (-4t)2 + (15+3t+500)2 (*)

Using the distance formula.

Differentiating with respect to t

2s ds/dt = 2 (-4t) (-4) + 2 (15 + 3t+500) (3) (**)

So as soon as t = 15

Calculate s making use of (*)Find ds/dt utilizing (**)

Sorry, typo. Woguy is at (500, -4t). So s^2 = 500^2 + <15 + 3t +4t>^2, so 2s ds/dt = 2 (15 + 7t) (7).
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