Solution for Climbers

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All you need to know is that Distance = Rate x Time.

Knowing that you traveled at a constant rate, the distance covered every two hours is the same, let's call it "N" miles. Since you reached the top at noon you know each of the distances (AB, BC, CD) equal N miles.

  |<- N miles ->|<- N miles ->|<- N miles ->|
  |_____________|_____________|_____________|
  A             B             C             D
 6 am          8 am         10 am         noon

The scouts passed you going up at point B at 8 a.m., then they passed you going down at 10 a.m. So in that 2 hours they traveled 3N miles.

Knowing they went 3N miles in 2 hours, you need to find out how long it takes them to go 2N miles (from B to D). Since you were both at point B at 8 a.m., this will tell you what time the scouts reached the peak.

 Time 	= Distance/Rate or
	= 2N miles / (3N miles / 2 hours)
	= 4/3 hours
	= 1 hour, 20 minutes

So the scouts reached the top at 8 a.m. plus 1 hour, 20 minutes or 9:20 a.m.

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