SOLUTION: A technician can assemble an instrument in 9.5 h . After working for 2.0 h , she is joined by another technician who, alone, could do the job in 7.5 h . How many additional hours a

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Question 1055488: A technician can assemble an instrument in 9.5 h . After working for 2.0 h , she is joined by another technician who, alone, could do the job in 7.5 h . How many additional hours are needed to finish the job?
Answer by htmentor(1343) About Me  (Show Source):
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The work rate of technician is 1 instrument per 9.5 h, or r1 = 1/9.5 = 2/19
The work rate of her assistant is 1 instrument per 7.5 h, or r2 = 1/7.5 = 2/15
The technician working for 2 hours alone has completed (2/19)*2 = 4/19 of the instrument.
Therefore, 15/19 remains to be completed.
Working together, their combined rate, r, is 2/19 + 2/15 = 30/285 + 38/285 = 68/285 instruments per hour.
They need to complete 15/19, or 225/285 instruments.
So r*t = 225/285
t = 225/285*285/68 = 225/68 = 3.31 hours