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Two way radio distance traveled word problem

Two children own two-way radios that have a maximum range of 2 miles. One leaves a certain point at 1:00 pm, waking due north at a rate of 4mi/hr. The other leaves the same point at 1:15pm traveling due south at 6 mi/hr. When will they be unable to communicate with one another?

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Edward A. | Math Tutor, Retired Computer Scientist and Technical CommunicatorMath Tutor, Retired Computer Scientist a...
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This is a disguised Distance, Rate, Time problem.
As always, first identify the quantities involved:
 
let t be the amount of time (in hours) it takes them to get to the 2 mile limit
let Df be the distance traveled by the first child
let Ds be the distance traveled by the second child
 
Next, translate the words into equations. This is tricky this time.
(first child distance, rate, time)
Df = t * 4
(second child distance, rate, time)
Ds = (t-(1/4)) * 6
(distances add up to 2)
Df + Ds = 2
 
Now, to solve this, substitute Df and Ds into the last equation
(t*4) + (t-(1/4)) * 6 = 2
 
Multiply these out, collect terms involving t, and solve for t. Add the amount of time to 1:00 PM to get the answer.