A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 108/17
A and B work for different numbers of hours a day, so the work is measured in hours: a person who needs \(n\) hours for the job does \(\frac{1}{n}\) of it in one hour, and when two work together their hourly work is added.
Hours each needs alone:
A: \(16\times6=96\) hours
B: \(12\times9=108\) hours
Working together:
Work in one hour \(\displaystyle =\frac{1}{96}+\frac{1}{108}=\frac{9+8}{864}=\frac{17}{864}\)
Hours needed \(\displaystyle =\frac{864}{17}\)
At 8 hours a day, days needed \(\displaystyle =\frac{864}{17\times8}=\frac{108}{17}\)