Question

Two surveyors with two-way radios leave the same point at 9:00
a.m., one walking due south at 3 mi/hr and the other due west at 4 mi/hr. how long can they communicate with one another if each radio has a maximum range of 6 miles?

Answer 1

Let they communicate with one another  for time t.

Please see the attached image.

We have been given that each radio has a maximum range of 6 miles. Hence, the hypotenuse of the triangle is 6.

We know the formula

$Distance = Velocity \times time$

Using this formula, we have

$AB=4t\\ BC=3t\\ AC=6$

Now, using Pythagorous theorem, we have

$(3t)^2+(4t)^2=6^2\\  \\ 9t^2+16t^2=36\\ \\ 25t^2=36\\ \\ t^2=\frac{36}{25} \\ \\ t=\frac{6}{5} \approx 1.20$

Therefore, they can communicate for 1.20 hours.