Multiple choice

Humans and robots can both perform a job but with different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

  1. 32

  2. 36

  3. 40

  4. 45
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A Correct answer
Explanation

Let H and R be the daily work of a human and a robot. 15H + 5R = 1/30. 5H + 15R = 1/60. Multiply first by 3: 45H + 15R = 3/30 = 1/10. Subtract second: 40H = 1/10 - 1/60 = 5/60 = 1/12. H = 1/480. 15H = 15/480 = 1/32. Time = 32 days.

AI explanation

Using the formula (15h + 5r) times 30 equals the total work, and (5h + 15r) times 60 equals the same total work, we set up the equation 450h + 150r = 300h + 900r. This simplifies to 150h = 750r, meaning one human equals five robots, or h = 5r. Substituting this into the first equation gives (75r + 5r) times 30 equals 2400r. To find the time for fifteen humans, which is 75 robots, we divide 2400r by 75r to get 32 days.

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