Multiple choice

Two workers, A and B, work on a project together for the first 5 days. Worker A can complete the project in 10 days, while Worker B can do it in 15 days. After 5 days, Worker A leaves, and Worker B completes the remaining work alone. Quantity A The total number of days taken to complete the project Quantity B 7 days

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
Explanation

A does 1/10 of the work per day, B does 1/15. Together, they do (1/10 + 1/15) = 5/30 = 1/6 of the work per day. In 5 days, they complete 5/6 of the work, leaving 1/6 for B. B takes (1/6) / (1/15) = 2.5 days to finish. Total time = 5 + 2.5 = 7.5 days, which is greater than 7.

AI explanation

Using the least common multiple method, let the total project be 30 units. Worker A has a rate of 3 units per day and Worker B has a rate of 2 units per day. Working together for 5 days, their combined rate of 5 units per day yields 25 completed units, leaving 5 units of remaining work. Worker B completes these 5 remaining units alone at a rate of 2 units per day, requiring 2.5 additional days. The total time taken to complete the project is the initial 5 days plus the 2.5 additional days, resulting in 7.5 days. Since 7.5 days is greater than 7 days, Quantity A is greater.

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