A man starts walking north at 2 ft/s from a point p. five minutes later a woman starts walking south at 4 ft/s from a point 500 ft due east of p. at what rate are the people moving apart 15 minutes after the woman starts walking? (round your answer to two decimal places.)
After 5 minutes (300 seconds): The man travels north by (2 ft/s)*(300 s) = 600 ft The woman, located at q, 500 east of p, begins walking south at 4 ft/s. The distance separating them is d₁ = √(600² + 500²) = 781.025 ft
After 20 minutes: The man has traveled for 20 minutes (1200 s). The woman has traveled for 15 minutes (900 s). The man has moved (2 ft/s)*(1200 s) = 2400 ft north of p. The woman has moved (4 ft/s)*(900 s) = 3600 ft south of q. The distance separating them is d₂ = √(6000² + 500²) = 6020.8 ft
The separation from d₁ to d₂ occurs in 15 minutes (900s). Therefore the rate of separation is Rate = (d₂ - d₁ ft)/(900 s) = (6020.8 - 781.025)/900 = 5.822 ft/s or Rate = (5.822 ft/s)*(60 s/min) = 349.32 ft/min
