Multiple choice

Two workers, A and B, are hired to complete a construction project. Worker A can complete the project in 20 days, while worker B can complete the project in 25 days. A and B start the work, however after working together for 5 days, worker A leaves due to unforeseen circumstances. To complete the remaining work, worker B hires worker C, who can alone complete the project in 30 days. How many more days will it take for B and C to complete the remaining project?

  1. 5.5 days

  2. 8.5 days

  3. 7.5 days

  4. 5 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/20, B's rate = 1/25. Together rate = 1/20 + 1/25 = 9/100. In 5 days, they do 5 * 9/100 = 45/100 = 9/20. Remaining work = 11/20. B and C rate = 1/25 + 1/30 = 11/150. Time = (11/20) / (11/150) = 150/20 = 7.5 days.

AI explanation

Using the fraction of work method, let the total work be the least common multiple of 20, 25, and 30, which is 300 units. Worker A's rate is 15 units per day and worker B's rate is 12 units per day, so in 5 days they complete 27 times 5 equals 135 units. This leaves 165 units of work, and worker C's rate is 10 units per day, making the combined rate of B and C equal to 22 units per day. Dividing 165 by 22 gives the time needed to finish the remaining project. The result is 7.5 days.

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