The most important variable is 4 miles per hour up hill. Down hill he can run 3 miles in the same time it takes time to run uphill. up hill 4 miles 1 hour so 2 miles up hill is 1/2 hour. Down hill he can run 3 miles in the same time it takes time to run up hill.. 2 miles up hill - 1/2 hour. So 1/2 hr up and 1/2 hr down = 1 hour.
Answer (13 of the original arrangements are duplicates now, as
AAAF F F FDDDDCC, AAF F F FDDDDCCA, ..., CAAAF F F FDDDDC
are identical): 900900/13 = 69300.
