working alone at their respective constant rates A completes a job in 4 hours and F completes a job in 3 hours. A and F worked together and completed the job in 2 hours.But while A worked the entire time F worked for some of the time and took 3 breaks of equal length. How many minutes long were F's breaks?

Let us assume the total work to be done is equal to 12 units. For the same job, it is given that
A completes it in 4 hours, so work rate of A = 3/hr
Similarly, work rate of F = 4/hr.
Which means that the work done by A and F is in the ratio 3:4 for any set period of time.
Both together completed it in 2 hours. So their work rate together = 12/2 = 6/hr
A worked the entire time, so A did 3 work every 1 hour. The remaining 3 work was done by F. But the work rate of F is 4. So he only worked for 3/4 of an hour or 45 mins. So, for the entire 2 hours he did not work for 30 mins. This is split into 3 equal breaks = 30/3 = 10 mins each