SOLUTION: Corbin Ecles and Connor Hayes have received walkie talkies for Christmas. If they leave from the same point at the same time, Corbin walking north at 2.5 mph and Connor walking ea

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Question 43975: Corbin Ecles and Connor Hayes have received walkie talkies for Christmas. If they leave from the same point at the same time, Corbin walking north at 2.5 mph and Connor walking east at 3 mph, how lone will they be able to talk to each other if the range of the walkie-talkies is 4 mi?
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
Let corbin's location be denoted by A, and Corbin's location denoted by B.
The coordinates of point A at any time "t" are (0,2.5t)
The coordinates of point B at any time "t" are (3t,0)
the distance between the two is the hypotenuse of the right-angled triangle with vertices points A, B and the origin (0,0).
the length of the hypotenuse ("L") can be found using L=sqrt%28x%5E2%2By%5E2%29
We can find L using the coordinates of points A and B, by substituting values for x and y:
L=sqrt%28%283t%29%5E2%2B%282.5t%29%5E2%29
We are looking for L=4
4=sqrt%28%283t%29%5E2%2B%282.5t%29%5E2%29
squaring:
16=%283t%29%5E2%2B%282.5t%29%5E2
16=%283t%29%5E2%2B%282.5t%29%5E2
16=15.25t%5E2
1.049=t%5E2
t=1.024hours
if you multiply the decimal (0.024) by 60, the answer is 1 hour and 1 minute; multiplying the decimal remaining by 60 again obtains the full solution: 1 hour, 1 minute, 27seconds