A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time? Let x be the distance (in miles) between point P and where the boat lands on the lakeshore. a. Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. b. What is the distance x = c that minimizes travel time? c. What is the least travel time.
I know that x is between 0 and 11, the velocity on the shore is 3 mi/hr, that the velocity on water is 2mi/hr. For x = 0, the total time would be about 6 hours. For x = 11, the time would be 6.16666 hours. The function should therefore be some quadratic. But how do I find this function? If I can find the function, I can use calculus to find the distance and the time that it would take. I would be grateful if someone explained the needed steps.