Question

A small island is 3 miles from the nearest point P on the straight shoreline of a large lake. If a women on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 15 miles down the shore from P in the least time?
the boat should be landed ? miles down the shore from P. (type exact answer)

Answer 1

Let the distance from P to the point of landing be x

Sqrt(3^2 + x^2) + 9-xx is the distance.

Sqrt(9+x^2)/2 + (9-x)/3 is the amount of time it takes.

Time is 4.12 if x = 2.7, which is the least