Multiple choice

Twelve identical machines, running continuously at the same constant rate, take $8$ days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by $2$ days?

  1. $2$
  2. $3$
  3. $4$
  4. $6$
  5. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = 12 machines * 8 days = 96 machine-days. To finish in 8 - 2 = 6 days, we need 96 / 6 = 16 machines. Since we have 12, we need 16 - 12 = 4 additional machines.

AI explanation

Using the formula M1 times D1 equals M2 times D2, the total work is 12 machines times 8 days, totaling 96 machine-days. The new time required is 8 days minus 2 days, which is 6 days, so the required number of machines is 96 divided by 6, equaling 16. The additional machines needed are 16 minus 12, resulting in 4.

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