SOLUTION: Tom takes 3 days to do a piece of work while jerry takes only one day for the same. Together, they both can finish the job in 15 days. In how many days tom will finish the work?

The key to the solution of the problem is to recognize (to realize) that there is the "entire job" and "the piece of job". 

Regarding "the piece of work", Tom's rate of work is  of "the piece of work" per day.

Jerry's rate of work is  = 1 of "the piece of work" per day, which means "one piece of work" per day.

Working together, these personages make  =  of "the piece of work" per day.

Hence, they spend  of the day, or 0.75 of the day, to complete this "piece of work", working together.

Since the entire job requires 15 day for Tom and Jerry to complete it working together, it means that the entire job is 
in  = 20 times larger (greater) than "the piece of work". Or, in other words, the entire work is equivalent to 20 "pieces of work".

Knowing it, you will easily find the answer to the question in the claim:

Tom will finish the job in 20*3 = 60 days working alone.