Question

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?

Answer 1

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