Let a, b, and c represent the running times of persons a, b, and c, respectively.
The problem statement describes several relationships:
... a + b + c = 66 . . . . . their combined time is 66 minutes
... b = 2 + 5a . . . . . . . . b's time is 2 minutes more than 5 times a's
... 2b + 4a = c . . . . . . . twice b's time plus 4 times a's time is equal to c's
These can be solved a variety of ways. One way is to use the second equation for b to substitute into the other equations. This gives ...
... a + (2+5a) + c = 66
... 2(2+5a) +4a = c
The first of these simplifies to
... 6a +c = 64
The second of these simplifies to
... 9a -c = -4
Adding these two equations together gives
... 15a = 60
... a = 4 . . . . . . . divide by 15
From above, b = 2 + 5a = 2 + 5·4 = 22
It took b 22 minutes to run that part of the race.