Let x be the total length of the tunnel, y be the distance the train is from the entrance of the tunnel, and v the rate this doofus is running at. The train speed is 60 mph and the guy is 0.4x into the tunnel at t=0. Length is measured in miles, time in hours, and speed in mph.
1. Time for train to reach tunnel entrance = time for the guy to run back to the entrance: y/60=0.4x/v
2. Time for train to reach tunnel end = time for the guy to run to end of tunnel: (x+y)/60=0.6x/v
From (2) we have v=0.6x*60/(x+y), which simplifies to v=36x/(x+y)
From (1) we have y=0.4x*60/v, which simplifies to y=24x/v
Inserting the latter into the former, we obtain v=36x/(x+24x/v), which simplifies to v=36/(1+24/v).
Multiplying both sides by the denominator, we get v(1+24/v)=36, which equates to v+24=36, and hence v=12 mph.
Answer: The guy runs at a rate of 12 mph (pretty fast!).