Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER man starts walking north at 2ft//s from a point P. Five minutes later a woman starts walking south at 5ft//s from a point 500ft due east of P. At what rate are the people moving apart 15min after he.woman starts walking? (Round your answer to two decimal places.) ft//s Entreantares finta Wateh it

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Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER man starts walking north at  2ft//s from a point  P. Five minutes later a woman starts walking south at  5ft//s from a point  500ft due east of  P. At what rate are the people moving apart  15min after he.woman starts walking? (Round your answer to two decimal places.)  ft//s Entreantares finta Wateh it

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Convert to seconds: Convert the time from minutes to seconds for both the man and the woman. The man starts walking and continues for 5 minutes before the woman starts, plus an additional 15 minutes after the woman starts walking. This is a total of 20 minutes for the man. 5 minutes + 15 minutes = 20 minutes Convert 20 minutes to seconds: 20 minutes * 60 seconds/minute = 1200 seconds. The woman walks for 15 minutes. Convert 15 minutes to seconds: 15 minutes * 60 seconds/minute = 900 seconds.Calculate distances: Calculate the distance each person has walked. The man walks at 2 ft/s for 1200 seconds. Distance = speed * time Distance_man = 2 ft/s * 1200 s = 2400 feet The woman walks at 5 ft/s for 900 seconds. Distance_woman = 5 ft/s * 900 s = 4500 feetDetermine positions: Determine the positions of the man and the woman relative to point P. The man is 2400 feet north of point P. The woman is 4500 feet south of point 500 feet east of P.Calculate north-south distance: Calculate the distance between the man and the woman in the north-south direction. Since the man is walking north and the woman is walking south, their distances add up in the north-south direction. Total north-south distance = Distance_man + Distance_woman Total north-south distance = 2400 feet + 4500 feet = 6900 feetUse Pythagorean theorem: Use the Pythagorean theorem to find the total distance between the man and the woman. The distance between the man and the woman forms the hypotenuse of a right triangle, with one leg being the total north-south distance and the other leg being the east-west distance (500 feet). Let d be the hypotenuse. d^2 = (Total north-south distance)^2 + (East-west distance)^2 d^2 = 6900^2 + 500^2 d^2 = 47610000 + 250000 d^2 = 47860000 d = sqrt(47860000) d ≈ 6918.26 feetCalculate rate of increase: Calculate the rate at which the distance between the man and the woman is increasing after 15 minutes the woman starts walking. The man and the woman are moving in perpendicular directions, so their speeds add up directly to give the rate at which they are moving apart. Rate = speed_man + speed_woman Rate = 2 ft/s + 5 ft/s = 7 ft/s

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