Talking through the problem and solving it

1. @ 1pm, the kid starts walking towards north at 4 miles/hr

2. @ 1:15pm, the distance between the kids is 1 mile (4 miles/hr => 1 mile/15 minutes)

3. @ 1:15pm, the other kid starts walking towards south @ 6 miles/hr

4. From the above instant, since the kids are going in opposite directions, the distance between them increases at the rate of (4 + 6) miles/hr => 10 miles/hr

5. For them to go out of range, they need to go 1 more mile apart

6. To cover 1 more mile @ 10 miles/hr, it takes 1/10th of an hour, which is 1/10 * 60 mins = 6 mins

7. Time when they go out of range = 1:15pm + 6 mins = 1:21pm

Hope this helps :)

Mahurshi Akilla