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
[tex]Distance = Velocity \times time[/tex]
Using this formula, we have
[tex]AB=4t\\ BC=3t\\ AC=6[/tex]
Now, using Pythagorous theorem, we have
[tex](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[/tex]
Therefore, they can communicate for 1.20 hours.
