A technician can assemble an instrument in 7.8 h. After working for 3 h, she is joined by another technician who can do the job himself in 7 hours. How many additional hours are required to finish the job?

1 Answer
Dahlia S.
Mar 16, 2018

2.27 hours

Explanation:

The first technician completes the job in 7.8 hours, meaning each hour she completes #1/7.8# of the job. This means that in the first 3 hours, she completes #3/7.8#, or about 38.46% of the job, meaning there is 61.54% of the job left when the second technician joins her.

The second technician can complete the job in 7 hours, meaning each hour he completes #1/7# of the job. To find the combined hourly progress of the two technicians, we simply add the progress that each of them would make in one hour.

#1/7.8+1/7=.271#

This means that they will complete 27.1% of the project every hour. Finally we divide the progress that they must complete by their hourly progress.

#0.6154/0.271=2.27# hours of work

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