Two way radio distance traveled word problem

Question

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?

Answer 1

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.