A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman 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 7 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lake shore.

Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. T(x) = ? What is the distance x=c that minimizes the travel time? What is the least travel time?

Question

A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman 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 7 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lake shore. 

 Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. T(x) = ? What is the distance x=c that minimizes the travel time? What is the least travel time?