Unnamed

On Monday at 8am, a mountain climber embarks on a climb up Mt Katahdin in 
Maine. It takes him 12 hours to complete the climb, so he arrives at the 
summit at 8pm, where he spends the night. At 9am the next morning, he heads 
down, and arrives at the base 9 hours later at 6pm.

The question is as follows:

Is there a spot on the mountain that the climber will pass at exactly the same 
time on both days?