SOLUTION: You are in a boat 2 miles from the nearest point on the coast. You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 mi

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Question 1127594: You are in a boat 2 miles from the nearest point on the coast. You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 miles per hour.
(a) Write the total time T (in hours) of the trip as a function of the distance x (in miles).
(b) Determine the domain of the function.
(c) Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window.
(d) Find the value of x that minimizes T.
(e) Write a brief paragraph interpreting these values.
I am not understanding this problem right now.

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


You didn't specify what the distance "x" is. I chose it to be the distance from the point on the shore closest to the boat to where the boat lands.

Then the distance rowing is sqrt%28x%5E2%2B4%29 and the distance walking is sqrt%28%28x-3%29%5E2%2B1%29.

Then, with the given rowing and walking speeds, the total time for the trip is

%28sqrt%28x%5E2%2B4%29%2F2%29%2B%28sqrt%28%28x-3%29%5E2%2B1%29%29%2F4

ANSWER a: T+=+%28sqrt%28x%5E2%2B4%29%2F2%29%2B%28sqrt%28%28x-3%29%5E2%2B1%29%29%2F4

ANSWER b: Algebraically, there are no restrictions on the domain of that function. However, logically the reasonable values for x should be between 0 and 3.

ANSWER c: A window of 0 to 3 for x and 1 to 2 for y produces a good graph.

ANSWER d: The minimum value of the function is when x=1.

ANSWER e: That is for you to do....