SOLUTION: 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 2 miles per hour and can walk 3 miles per hour
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Question 1141836: 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 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) =
You can put this solution on YOUR website! 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 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.
the distance rowed is the hypotenuse of 3 & x, and the distance walked is 10-x
time = dist/speed
T(x) = +
(B) What is the distance x = c that minimizes the travel time?
Minimum x = 2.75 mi, travel time: 4.45 hrs (green)
Note:
The answer to this problem requires that you enter the correct units.
c = 2.75 mi
(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 : 4.45 hrs
(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) =
Actually, I don't recall this.
