SOLUTION: Please help me with this problem: You are on a island in Lake Mercedes two miles from the coast. The nearest point on the coast is point P. The coast is a straight line for ten

Question 916920: Please help me with this problem:
You are on a island in Lake Mercedes two miles from the coast. The nearest point on the coast is point P. The coast is a straight line for ten miles on each side of P. You are to travel to a certain point Q in the shortest time. This point Q is located three miles along the coast from P than one mile inland. You can row at 2mph and walk at 4mph. Find the distance x from P where you should land your boat to travel from the island to Q in the least time. Hint use graphics utility.
If your able to help can you please explain how to do the problem and how to set it up.
Thank you
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
An explanation really depends on a good drawn figure. You'll best have to make one. Mine (not convenient to show here) uses a shore arrival point between P and the shore's reference point for the inland, Q. This is, the arrival point on shore is less than three miles away from P on the shore.

That gives a right triangle. 2 miles MP, x distance along the shore from P; and the expression for this rowing distance is .

The shore reference point being 3 miles away from P, another triangle has sides (3-x) and 1, so the hypotenuse is , which is the walking distance.

Uniform Rates for Travel has the rule RT=D for rate time distance. You have two different distances, each at a different rate of travel.
T=D/R, and having two such time quantities corresponding to each distance, you have a total time function:

The necessary analysis really must use the drawing, labeling parts and lengths, and identifying the needed Right triangles, and then you could formulate the function for total time. Difficult to give a drawing here.

This can be a derivative Calculus problem, but you can use your graphing calculator.
RELATED QUESTIONS
I need help with this problem please John is on an Island in Lake Cavenacci three miles... (answered by ankor@dixie-net.com)

You are in a boat a miles from the nearest point on the coast (see figure). You are to go (answered by ankor@dixie-net.com)

There is a small island in the middle of a 100m wide river and a tall tree stands on... (answered by Theo)

You are in a boat 2 miles from the nearest point on the coast. You plan to travel to... (answered by greenestamps)

On December 26, 2004, an earthquake generated tsunamis off the coast of the island of... (answered by richwmiller)

can you please help me with this problem the expression 8m+5 represents the total cost... (answered by stanbon)

Please help me solve this word problem: Joe is kayaking on a lake. He is 2 miles from... (answered by KMST)

can you please help me solve this problem?: A lighthouse is located on a small island (answered by ankor@dixie-net.com)

A small island is 4 miles from the nearest point P on the straight shoreline of a large... (answered by KMST)