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When Ben will reach the end of the hike, Peter will be at the mid of the hike distance.
In other word, when Ben is at the point with coordinate 24 kilometers from the starting point, Peter is only
at 12 kilometers distance from the starting point.
Now Ben turns and goes back to meet Peter; Peter continue his way from that mid point.
At this moment, the distance between them is 24-12 = 12 kilometers.
Since Ben walks twice as fast as Peter, they will meet at the point, which separate these 12 kilometers
distance in ratio 2:1.
It means that the meeting point is at 4 km distance from the midpoint in direction to the end of the hike.
ANSWER. They meet each other at the point, which is 12+4 = 16 kilometers away from the starting point.
Solved.
So, this problem admits simple mental solution.