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A man starts walking north at 2ft/s2\,\text{ft/s} from a point PP. Five minutes later a woman starts walking south at 5ft/s5\,\text{ft/s} from a point 500ft500\,\text{ft} due east of PP. At what rate are the woman and man separating when the woman starts walking? (Round your answer to two decimal places.)\newlineEnter a number:______ft/s\text{ft/s}

Full solution

Q. A man starts walking north at 2ft/s2\,\text{ft/s} from a point PP. Five minutes later a woman starts walking south at 5ft/s5\,\text{ft/s} from a point 500ft500\,\text{ft} due east of PP. At what rate are the woman and man separating when the woman starts walking? (Round your answer to two decimal places.)\newlineEnter a number:______ft/s\text{ft/s}
  1. Rephrase Problem: First, let's rephrase the problem into a single question_prompt: "At what rate are the man and woman separating from each other after the woman starts walking?"
  2. Calculate Speeds: The man is walking north at 2ft/s2\,\text{ft/s}, and the woman starts walking south at 5ft/s5\,\text{ft/s}. Since they are walking in opposite directions, their speeds will add up when calculating the rate at which they are separating.
  3. Add Speeds: To find the rate at which they are separating, we add the man's speed to the woman's speed.\newlineRate of separation = Man's speed + Woman's speed\newlineRate of separation = 2ft/s+5ft/s2 \, \text{ft/s} + 5 \, \text{ft/s}
  4. Perform Calculation: Perform the calculation to find the rate of separation. Rate of separation = 2ft/s+5ft/s=7ft/s2\,\text{ft/s} + 5\,\text{ft/s} = 7\,\text{ft/s}
  5. Final Answer: The rate at which the man and woman are separating after the woman starts walking is 7ft/s7\,\text{ft/s}. This is the final answer, and it is already rounded to two decimal places as required.

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