Corhin Eckles and Connor Hayes have recieved walkie talkies

Corhin Eckles and Connor Hayes have recieved walkie talkies for Christmas. If they leave from the same point at the same time, Corhin walking north at 2.5 mph and Connor walking east at 3 mph, how long will they be able to talk to each other if the range of the walkie-talkies is 4 mi?

Solution

Corhin DATA:
distance= x miles; rate=2.5 mph; time=d/r= x/2.5
Connor DATA:
distance= y miles; rate=3 mph; time=y/4
EQUATIONS:
1) x^2+y^2=4^2
2) x/2.5 = y/4
Using 2) you get y=4x/2.5
Substitute into 1) to get x^2+(4x/2.5)^2=16
x^2+(16x^2/6.25)=16
6.25x^2+16x^2=16(6.25)
22.25x^2=100
x^2=100/22.25=4.49...
x=2.12 hrs.
x/2.5= 0.85 hrs. = 50.87 minutes
This is Corhin\'s time, but it is the same for Connor.