Soo… if the mechanic and his assistant can assemble an engine in 2 1/4 hrs, and the assistant can assemble the engine by himself in six hours, then (this here is the trick!) together the mechanic and his assistant can do 1/(2 1/4) of the job per hour, and the assistant alone can do 1/6 per hour. How much then can the mechanic do per hour if he works alone?

To find out how much the mechanic can do alone per hour, subtract what the assistant can do by himself per hour from what both the mechanic and assistant can do together per hour: 1/(2 1/4) – 1/6 = 1/(2.25) – 1/6 = 1/(9/4) – 1/6 = 4/9 – 1/6 = 8/18 – 3/18 = 5/18. The mechanic can do 5/18 of the job per hour. Now let “t” stand for how long the mechanic takes to assemble the engine by himself. He can do 1/t per hour, so 5/18 = 1/t. Flip the equation, and you get that t = 18/5 = 3.6 hours. That is:

hours to completely assemble the engine:

together: 2 1/4 hrs

assistant: 6

mechanic: t

completed per hour:

together: 1/(2.25)

assistant: 1/6

mechanic: 1/t

subtracting their labor:

1/(2.25) – 1/6 = 1/t

5/18 = 1/t

18/5 = t

They can complete the job together in just over 3 1/2 hours.

HOPE THIS HELPS!!!!