A man starts walking north at 3 ft/s from a point

Question

A man starts walking north at 3 ft/s from a point P. Five minutes later a woman starts walking south at 7 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? (Round your answer to two decimal places.)

Answer 1

Draw a figure with a vertical line heading up and one heading down and 500 f' between them.

The man walking north walks 3(t+5) feet and the woman heading south walks 7t.

The distance between them is d and d² = [3(t+5) + 7t]² + 500²

^{Collect terms and differentiate d with respect to t. Then you will have all the information you need to answer the question.}