F completes one rotation in 1 hr
S completes 1/2 in 1 hr
T completes 1/3 in 1 hr
together they complete
1+1/2+1/3 rotations = 11/6 rotation in one hr
So they meet after 60 * 11/6 minutes = 110
I do not think that this is correct logic. 11/6 is just the total of the rotations finished by all the three hands IN ONE HOUR. But all three will not be in the same position. In ONE HOUR, the first hand will again be in 12 oclock position, the secon will be on 6 and the third ahnd would be on 4. They will not conside in any way.