You hike uphill at a rate of 200 feet per minute. Your friend hikes downhill on the same trail at a rate of 250 feet per minute. How long will it be until you meet? The friend at the bottom is starting at 100 feet and hiking up. The friend at the top is starting at 1800 feet and hiking down.

in t = 3.77 min they will met each other

Explanation:

If your friend and you start at coordinate x₁ and x₂ respectively, then if your friend is at a distance xF from the bottom

xF = x₁ - v₁*t = 1800 ft - 250 ft/min * t

and you are at a distance xM from the bottom

xM = x₂ + v₂*t = 100 ft + 200 ft/min * t

then both find at xM=xF

x₂ + v₂*t = x₁ - v₁*t

t = (x₁ - x₂) / (v₁+v₂) = (1800 ft - 100 ft) / (250 ft/min + 200 ft/min) = 3.77 min

t = 3.77 min