Kai is on an island 3 miles from the nearest point on a straight shoreline of the ocean, a town lies 10 miles down the shore from that point. Kai will row to shore and then run down the shore to the town. She wants to minimize the time spent traveling. If she rows at 3 mph and runs at 5 mph determine the point on the shore, she should land to reach the town in the least amount of time. Round the solutions to two decimal places. a. Define the variable(s) and state the objective function b. What is the interval of interest (domain) For your objective function? c. What is the minimum time it will take Kai to reach the town?

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.8: Rate-time-distance Problems
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Kai is on an island 3 miles from the nearest point on a straight shoreline of the ocean, a town lies 10 miles down the shore from that point. Kai will row to shore and then run down the shore to the town. She wants to minimize the time spent traveling. If she rows at 3 mph and runs at 5 mph determine the point on the shore, she should land to reach the town in the least amount of time. Round the solutions to two decimal places. 

a. Define the variable(s) and state the objective function

b. What is the interval of interest (domain) For your objective function?

c. What is the minimum time it will take Kai to reach the town?

 

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if she uses a motorboat to travel from the island to the shore at a speed of 22 mph, where should she exit the water and what is the minimum time it would take to reach town?

 

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