WALKIE TALKIES AND DIRECTIONS

Question

Sam and Sara start at home. Sam travel east at 4mph and Sara travels south at 5mph. They have a two-way radio with a range of 5 miles. How long after they start do they fall out of radio contact range?

Answer 1

Sam travel east at 4mph and Sara travels south at 5mph

Sam's location is

x = 4 * h towards east.

Sara's location is

y = -5 * h towards south.

Since east and south are perpendicular, their distance is, using Pythagorean theorem,

d = sqrt(x^2 - y^2) = sqrt(16 h^2 + 25 h^2)

They will loose radio contact at 5 miles. Then

5 = sqrt(16 h^2 + 25 h^2) . Take the square of both sides

25 = 41 h^2

h^2 = 25/41

h = sqrt(25/41) = 5 / sqrt(41) = 5 / 6.4 = 0.78 hours

Or 0.78 * 60 ~ 47 minutes