A can complete a piece of work in 8 days, and B can complete the same work in…
2024
A can complete a piece of work in 8 days, and B can complete the same work in 10 days. If A and B work together, how long will they take to complete the work?
Answer: B. \(4\frac{4}{9}\) days — ConceptA worker's one-day work rate is the reciprocal of the time taken to complete the whole job alone. When workers contribute independently to the same job…
- A.
6 days
- B.
\(4\frac{4}{9}\) days
- C.
\(4\frac{1}{5}\) days
- D.
\(5\frac{1}{2}\) days
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
A worker's one-day work rate is the reciprocal of the time taken to complete the whole job alone.
When workers contribute independently to the same job at the same time, their work rates add, and the completion time is the reciprocal of the combined rate.
Application
Let the total work be 1 unit. The one-day rates of A and B are \(\frac{1}{8}\) and \(\frac{1}{10}\) of the work.
Their combined rate is \(\frac{1}{8}+\frac{1}{10}=\frac{5+4}{40}=\frac{9}{40}\) of the work per day.
Therefore, the required time is \(1\div\frac{9}{40}=\frac{40}{9}\) days.
Converting the improper fraction gives \(\frac{40}{9}=4\frac{4}{9}\) days.
Cross-check
In \(\frac{40}{9}\) days, the combined work is \(\frac{40}{9}\times\frac{9}{40}=1\) complete job, so the result is consistent.
Result
A and B complete the work in \(4\frac{4}{9}\) days.