Multiple choice

Bob and Smith together can finish a piece of work in 8 days. Both start the work together. After 3 days, Bob falls ill. Smith alone finishes the remaining work in 15 days. How many days would Bob take working alone to finish that work?

  1. 10 days

  2. 11 days

  3. 12 days

  4. 15 days

  5. 18 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Together rate = 1/8. In 3 days, they do 3/8 of work. Remaining = 5/8. Smith does 5/8 in 15 days, so Smith's rate = (5/8)/15 = 1/24. Bob's rate = 1/8 - 1/24 = 3/24 - 1/24 = 2/24 = 1/12. Bob takes 12 days.

AI explanation

Bob and Smith complete 3/8 of the work in 3 days, leaving 5/8 of the work remaining. Since Smith finishes this 5/8 portion in 15 days, Smith's daily work rate is (5/8) / 15 = 1/24. Bob's daily rate is found by subtracting Smith's rate from their combined rate: (1/8) - (1/24) = 2/48 = 1/24, which is incorrect because (1/8) - (1/24) equals 1/12. Thus, Bob's daily rate is 1/12, meaning Bob alone would take 12 days to finish the work.

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