Solution: (1) If the cooperation between two people takes X days to complete, the equation can be drawn from the meaning of the question:1/4x+1/6x =1.

Solution: x= 125=2.4.

That is, it will be completed in 2.4 days.

(2) If the apprentice did it one day first, then the apprentice has already done one-sixth of the total workload that day, leaving five-sixths of the workload.

After a day's work, the apprentice will have to work for another y days to finish the rest of the workload.

The equation can be obtained from the meaning of the question: 1/4y+ 1/6y=5/6.

Solution: y=2,

Therefore, the apprentice * * * completed1/6× 2+1/6 =1/2 of the total workload.

1/4×2= 1/2 of the total workload completed by the master.

Answer: All the work done by master and apprentice is 1/2, and each person has to pay 450/2=225 yuan.