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 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 10 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.

(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 $T''(c)$?
$T''(c)$ =

Hint: