Question

Two surveyors with two-way radios leave the same point at 9:00am., one walking due south at 2 mi/hr and the other due west at 5 mi/hr. How long can they communicate with one another if each radio has a maximum range of 10 miles?

Answer 1

Set up a right triangle. After 1 hour, the triangle will have one leg of 2, the other 5, and a hypotenuse of sqrt(4+25) = 5.385

Now, after t hours, the sides will be 2t and 5t, and the hypotenuse will be 5.385t

We want to find out when they are 10 mi apart; that's just the length of the hypotenuse.

5.385t = 10
t = 1.857 hrs = 1 hr 52 min