Multiple choice

P, Q, and R can complete a task together in 15 days. P and R can complete the task together in 40 days. How many days will Q take to complete the task alone?

  1. 30 days

  2. 24 days

  3. 21 days

  4. 25 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given 1/(P+Q+R) = 1/15 and 1/(P+R) = 1/40. Then 1/Q = 1/15 - 1/40 = (8-3)/120 = 5/120 = 1/24. Thus, Q takes 24 days.

AI explanation

Using the work rate method, P, Q, and R complete 1/15 of the task per day, while P and R complete 1/40 per day. Subtracting the combined rate of P and R from the total rate gives Q's daily rate: (1/15) - (1/40). Finding a common denominator of 120, this becomes (8/120) - (3/120) = 5/120, which simplifies to 1/24. Therefore, Q takes 24 days to complete the task alone.

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