A and B can together complete a task in 20 hours, after 5 hours A leaves. B…
2023
A and B can together complete a task in 20 hours, after 5 hours A leaves. B takes 45 hours to finish the remaining task. How many hours would A have taken to complete the entire task, if he worked alone from the beginning?
Answer: A. 30 hours — ConceptA person’s work rate is the fraction of the whole task completed per hour. Rates add when people work together, and work completed equals rate…
- A.
30 hours
- B.
40 hours
- C.
48 hours
- D.
60 hours
Show answer & explanation
Correct answer: A
Concept
A person’s work rate is the fraction of the whole task completed per hour. Rates add when people work together, and work completed equals rate multiplied by time.
Application
A and B together have rate 1/20 task per hour. In 5 hours they complete 5 × 1/20 = 1/4 of the task, leaving 3/4.
B completes the remaining 3/4 in 45 hours, so B’s rate is (3/4) ÷ 45 = 1/60 task per hour.
Therefore A’s rate is 1/20 − 1/60 = 2/60 = 1/30 task per hour.
Cross-check
At rates 1/30 and 1/60, A and B together work at 1/20 task per hour. Five hours completes 1/4, and B then needs 45 hours to finish 3/4, matching the given data.
Result
Thus A alone would complete the whole task in 30 hours.