Worker X completes a task in 8 days and worker Y completes the same task in 10…
2022
Worker X completes a task in 8 days and worker Y completes the same task in 10 days. If both X and Y work together, in how many days they will complete the task?
- A.
40/10 days
- B.
40/9 days
- C.
40/7 days
- D.
40/8 days
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept: When a worker finishes a job in n days, that worker's one-day work (rate) is 1/n of the job. The rates of people working together ADD UP, and the total time to finish together is the reciprocal of the combined one-day rate.
X finishes in 8 days, so X's one-day work = 1/8 of the task.
Y finishes in 10 days, so Y's one-day work = 1/10 of the task.
Working together, their one-day work adds: 1/8 + 1/10. Taking the common denominator 40 gives 5/40 + 4/40 = 9/40 of the task per day.
Time to finish together = reciprocal of the combined one-day work = 1 / (9/40) = 40/9 days.
Cross-check: in 40/9 days, X does (1/8)(40/9) = 5/9 and Y does (1/10)(40/9) = 4/9; 5/9 + 4/9 = 1 whole task, which confirms the result.