Sam accepted a job to brick a new home. he calculated that he can complete the job in 4 days. he hired a trainee to assist him. he has seen the trainee work and estimates that the trainee working alone would take 6 days to complete the job. how much time should the two of them working together need to brick the house? (round your answer to the nearest tenth.)

This is the concept of proportionality, we are required to calculate the total time it will take the two men to complete the job given that:
Sam would take 4 days and the trainee would take 6 days;
Here proceed as follows;
Proportion of worked completed by Sam in 1 day will be:
1/4

Proportion of work completed by the trainee in 1 day will be:
1/6

Proportion of worked completed by them working together in 1 day will be:
1/6+1/4
=5/12

Time taken for the to complete the entire wall will be:

12/5
= 2 2/5 days