Although I used to think I knew everything about work problems, I must admit it took me a while before reaching the answer. Therefore, let me show my approach for those who still have problems with this type of questions.

Please, bear with me.

Let X be the time it takes a worker to perform a task alone. Then, 3X - time of an apprentice. 1/X - worker's hourly rate and 1/3X - that of an apprentice.

Substitute variable into an equation:

1/X+1/X+1/X+1/3X=1/3 (Watch it!, it's not 3 as I did originally)

10/3X=1/3

X=10 => time of an apprentice = 30 hours.

Now, new conditions are 2 workers and 2 apprentices.

A new equation looks as follows:

1/10+1/10+1/30+1/30=Y

8/30=Y (this is the amount of work a given group can complete in an hour's time). => reverse the ratio to get the total amount of time.

30/8=3and6/8 hours

3 and 6/8 hours - 3 hours = 6/8 hours (or 45 minutes)

Special thanks to Stolyar. Beautiful questions!

It's a pleasure to seeing Him here.

_________________

Respect,

KL