Step-by-step answer:
Answer to problems of this kind is the reciprocal of the harmonic mean of the time required.
We need to find the average of the speeds, not the average of the time.
The respective speeds are 1/3 and 1/4.
The average of the speeds is therefore (1/3+1/4)/2 = 7/24 (harmonic mean of the time taken).
The time required is therefore the reciprocal of the unit speed,
T = 1/(7/24) = 24/7 = 3 3/7 minutes, or approximately 3.43 minutes.