Multiple choice

A, B and C can build a wall in 12 days together. C is four times as productive as B and A alone can build the wall in 48 days. In how many days can A and B working together build the wall?

  1. 20

  2. 30

  3. 80

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A+B+C = 1/12. A = 1/48. B+C = 1/12 - 1/48 = 3/48 = 1/16. C = 4B. So B+4B = 5B = 1/16 => B = 1/80. A+B = 1/48 + 1/80 = 5/240 + 3/240 = 8/240 = 1/30. Time = 30 days.

AI explanation

Let the one day work of A, B and C be a, b and c. Given that a plus b plus c equals 1/12 and a equals 1/48, we have b plus c equals 1/16. Since C is four times as productive as B, c equals 4b, so 5b equals 1/16 and b equals 1/80. The combined one day work of A and B is 1/48 plus 1/80, which equals 8/240 or 1/30. The time A and B take together to build the wall is 30 days.

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