Answer :
Answer:
The answer is 21 minutes
Step-by-step explanation:
We use the equation Xf = Xo + vt
1) At 1:00 PM, child one leaves the starting point heading north at a constant velocity of 6 mi/hr or .1 [mi/min] (divide by 60 to convert from [mi/hr] to [mi/min])
2) He walks for 15 minutes before kid 2 starts walking. In 15 minutes he is able to cover 1.5 [mi]
- [tex]x_{1f1} =x_{o} +v_{1} t_{1} \\x_{1f1} =0+.1(15)\\x_{1f1} =1.5 [mi][/tex]
3) Now, child 2 starts walking and we know that when the range reaches 3 miles, they won´t be able to communicate. So the sum of the final position of child 1 and child 2 must be 3[mi]
- Child 1 final position => [tex]x_{1f} = x_{1f1} +v_{1} t\\x_{1f} =1.5+v_{1} t[/tex]
- Child 2 final position => [tex]x_{2f} =0+v_{2} t[/tex]
4) Sum the equations and equate to 3
- [tex]x_{1f} +x_{2f} =3[/tex]
5) Substitute the values we already know
- [tex]1.5+v_{1} t+v_{2}t=3\\ 1.5+.1t+.15t=3\\1.5+.25t=3\\t=\frac{3-1.5}{.25} \\t=6 [min][/tex]
6) in 15 + 6 minutes they will be 3miles apart
7) In 21 minutes they will still be able to communicate with one another.