Lesson A kayaker and an orca - simple, elegant and unexpectedly short solution

A kayaker and an orca - simple, elegant and unexpectedly short solution

Problem 1

Let 't' be the time under the problem's question.


To get the meeting point, the kayaker paddled 3t miles to the east.
while the orca swam 10t miles to the North.


According to the problem, these distances, 3t miles and 10t miles, 
are the legs of a right-angled triangle, whose hypotenuse is 1 mile.


So, we write the Pythagorean equation

     +  = 1,

     +  = 1,

     = 1,

     = ,

    t =  = 0.095782629 of an hour, or 0.095782629*60 = 5.746957711 minutes.


ANSWER.  The time is about 5.747 minutes.