P makes 10 rev/min , therefore 1/6 th rev per sec
Q makes 40 rev/min, therefore 4/6 th rev per sec
hence for a sec difference in rev is 3/6 th rev per sec ( 1/2 rev per sec)
so after 12 secs the difference in the rev will be 6 rev per sec.

Since the question is asking for seconds, convert everything into seconds now instead of doing so once you get your answer.

rate for P = 1/6 and rate for Q = 2/3

Just set up rate, time, work table and plug in the variables. You'll end up with two equations:

1) w = 1/6t [for P]

2) w + 6 = 2/3t [for Q]

Substitute P into Q, and you get:

1/6t + 6 = 2/3t

t = 12