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 3 miles per hour and can walk 4 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 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 3 miles per hour and can walk 4 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)T(x) that describes the total amount of time the trip takes as a function of the distance xx.
T(x)= (include units)
(b) What is the distance x=c that minimizes the travel time?
(note: careful to consider the domain of T(x) on which we are looking for the minimum. It could make a difference.)
c= (include units)
(c) What is the least travel time?
The least travel time is (include units)
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