A man in a rowboat is at point P, 5 miles away ... below

Question

A man in a rowboat is at point P, 5 miles away from the nearest point A on a straight line shore. He wishes to reach a point B, six miles from A along the shore, in the shortest possible time. Where should he land on the shore line if he can row at 2 mi/h and run at 6 mi/hr?

Answer 1

Draw a figure.

Then the time of travel becomes

sqrt(x² + 25)/2 + 6(6-x)/6 = T

where x is the distance from point A to his landing point.

Set dT/dx = 0 and solve for x to get your answer.

Answer 2