I claim it can be done in 17 minutes.
First, 2 minute man and 1 minute
man cross. Time = 2 minutes
Now send 2 minute man back. Time = 4 minutes.
10 minute man and 5 minute man hobble
across. Time = 14 minutes.
1 Minute man grabs the flashlight and sprints back to the first side. Time = 15 minutes.
2 minute man and 1 minute man hurry to the far side just as the battery
dies. Now they've all safetly crossed in 17 minutes, but they're stuck in the woods without a flashlight. Hopefully the moon
will come out.