Hermione wrote:

A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24

B. 1:34

C. 1:44

D. 1:54

E. 2:14

Let the qualified worked do 20 units/hr

=> well = 100 units

also, apprentices = 3/4*20 = 15 units/hr

and trainees = 1/5*20 = 4 units/hr

hence, team = (20 + 15*2 + 4*2) = 58 units/hr

we need to get the time of doing 100 units if 58 units are done in 1 hr.

=> 60*100/58 = 103.4 minutes or ~1 hr 44 mins (option C)

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Illegitimi non carborundum.