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Difficulty: EasyInverse Proportions

Match each military work scenario with the correct time it would take to complete the task. Assume all personnel work at the same constant rate.

  • 2 mechanics take 6 hours to repair an engine. How many hours will it take 4 mechanics?3 hours
  • 3 medics take 8 hours to inventory supplies. How many hours will it take 6 medics?4 hours
  • 4 logisticians take 5 hours to load a transport. How many hours will it take 10 logisticians?2 hours
  • 5 engineers take 6 hours to clear a path. How many hours will it take 6 engineers?5 hours

Answer

The 4 mechanics will take 3 hours, the 6 medics will take 4 hours, the 10 logisticians will take 2 hours, and the 6 engineers will take 5 hours.
Each scenario is an inverse proportion problem where the product of workers and time is a constant (total work). To find the new time, multiply the original workers by the original hours, then divide by the new number of workers.

Step-by-Step Solution

1
Calculate the constant total work for each scenario.
Scenario 1: 12 hours. Scenario 2: 24 hours. Scenario 3: 20 hours. Scenario 4: 30 hours.
In inverse proportions, the product of workers and time is a constant (representing the total work required).
2
Divide the total work by the new number of workers.
12/4 = 3 hours; 24/6 = 4 hours; 20/10 = 2 hours; 30/6 = 5 hours.
Since the total work remains constant, dividing it by the available workforce yields the new time.

Key Concept

Inverse Proportions
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Topics

Inverse Proportions

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