A small island is 3 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 12 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 lakeshore. Hint: time is distance divided by speed.

(A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x.
T(x) =


(B) What is the distance x=c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units.
c =
.

(C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units.
The least travel time is
.

(D) Recall that the second derivative test says that if T′(c)=0 and T″(c)>0, then T has a local minimum at c. What is T″(c)?
T″(c) =