Border Patrol Practice Exam

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Prepare for the Border Patrol Exam with our comprehensive quiz. Use flashcards and multiple choice questions to master the material. Enhance your chances of passing with informative hints and explanations.

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How long would it take Officer K and Officer M to complete a task together if Officer K takes 8 hours and Officer M takes 10 hours to complete it individually?

9 hours
8 1/9 hours
4 4/9 hours
6 3/4 hours

The correct answer is: 4 4/9 hours

To determine how long it takes for Officer K and Officer M to complete the task together, we can use the concept of their combined work rates. Officer K completes the task in 8 hours, which means their work rate is 1/8 of the task per hour. Officer M, taking 10 hours, has a work rate of 1/10 of the task per hour. When these two officers work together, we can add their rates to find their combined work rate: 1/8 + 1/10 can be calculated using a common denominator. The least common multiple of 8 and 10 is 40, so we convert the fractions: 1/8 = 5/40 and 1/10 = 4/40. Adding these rates together gives us: 5/40 + 4/40 = 9/40. This combined work rate means that together, they complete 9/40 of the task in one hour. To find out how long it will take for them to finish the entire task, we can take the reciprocal of their combined rate: Time = 1 / (9/40) = 40/9 hours. This is equal to 4 and 4/9 hours,