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

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(13198) (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 and the distance walking is .

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

ANSWER a:

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....
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