Question

A visitor is staying in a cabin that is 3 miles west of the closest point on a shoreline to a coral reef. The coral reef is 2 miles due south of the shoreline. The visitor plans to travel from the cabin to the coral reef by running and swimming. If the visitor runs at a rate of 7 mph and swims at a rate of 2 mph, how far should the visitor run to minimize the time it takes to reach the coral reef

Answer 1

Answer:

3.6miles

Step-by-step explanation:

Given:

distance of tent from the closest point on shore-line, d=3miles.

distance between shoreline point and coral reef, x=2miles

The shortest distance (say l) that the visitor runs towards the reef in order to swim a minimum distance which takes least time.

$\therefore l^2=d^2+x^2\\l=\sqrt{3^2+3^2} \\l=3.6\ miles$

Now on reaching at the shore at this point the visitor will have to swim the least distance due east to reach coral reef.