work formula

[demoskopico]

A qualified worker digs a well in 5 hours. He invites 2 apprentices who work as fast and 2 trainees who work as fast as he does. If the five-person team digs the same well, how much time does the team need to finish the job?
 1:20
 1:30
 1:40
 1:50
 2:10

Follow a basic approach: Work=Rate*time

Q is a rate of a qualified worker
3/4 Q that of an apprentice
1/5 Qthat of a trainee
When people work together, their rates are added. The work is the same, which leads to:

W=5Q=(Q+3/2 Q + 2/5 Q)T

5=29/10 * T


So, or 1:40.



anyway, at the course I learnt that for work cases we could apply the formula (A+B)/AB

I don't come with the same reasult anyway. Is this formula applicable any time? In cases with more than 2 people/machines, is better the approach above?

[kevin]

A qualified worker digs a well in 5 hours. He invites 2 apprentices who work as fast and 2 trainees who work as fast as he does. If the five-person team digs the same well, how much time does the team need to finish the job?
 1:20
 1:30
 1:40
 1:50
 2:10

Follow a basic approach: Work=Rate*time

Q is a rate of a qualified worker
3/4 Q that of an apprentice
1/5 Qthat of a trainee
When people work together, their rates are added. The work is the same, which leads to:

W=5Q=(Q+3/2 Q + 2/5 Q)T

5=29/10 * T


So, or 1:40.



anyway, at the course I learnt that for work cases we could apply the formula (A+B)/AB- is this formula correct?
I don't come with the same reasult anyway. Is this formula applicable any time? In cases with more than 2 people/machines, is better the approach above?


Note that the question does not include the fractions that the solution reflects. The formula in the course was as follows: If two machines, which take respectively t1 and t2 hours to complete a task (each working at a constant rate), together, they will take t1t2/(t1+t2) hours to complete said task. For example if Marco can paint a room in 3 hours and Paolo can do so in 5 hours, it would take them 15/8 hours to do so together