How Officers K and M Team Up for Efficient Task Completion

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?

• A. 9 hours
• B. 8 1/9 hours
• C. 4 4/9 hours
• D. 6 3/4 hours

Answer: (C)

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,

When it comes to teamwork—not just in the field, but in tackling tricky math problems too—let’s take a closer look at how two law enforcement officers, K and M, can better finish a task together. How long would it take these two officers to finish a task if Officer K takes 8 hours alone and Officer M takes 10 hours? You might wonder what happens when you combine their efforts.

Here’s the thing: the correct answer is 4 4/9 hours. But what’s the story behind that number? By analyzing how long it takes each officer to work independently, we can create a powerful picture of teamwork in action.

Start by thinking of their work rates—what on earth does that mean? Time for a quick refresher! Officer K, completing a task in 8 hours means, quite simply, he finishes 1/8 of a task each hour. Officer M, on the other hand, takes a bit longer at 10 hours, working at a rate of 1/10 for every hour.

Ready for the fun part? When these two join forces, it’s all about adding those rates together! That’s right, you can simply combine their individual rates into one powerhouse work rate. Let’s break it down:

1. Convert both fractions to have a common denominator. The least common multiple of 8 and 10 is 40.

So, here’s the math magic:

• Officer K’s work rate: 1/8 = 5/40

• Officer M’s work rate: 1/10 = 4/40

Adding those together gives:

5/40 + 4/40 = 9/40. This combined work rate means that together, they complete 9/40 of the task in just one hour.

Now, here’s the real clincher: to find out how long it’ll actually take them to finish the whole task, we take the reciprocal of that combined rate. Sounds fancy, right? Time = 1 / (9/40) = 40/9 hours.

Breaking that down gives us 4 and 4/9 hours—easy peasy, lemon squeezy!

Understanding how to tackle situations where teamwork is vital makes you not only better at math but also at your job in law enforcement. And let’s be real—who doesn’t want to boost their efficiency? Time is often a precious commodity, particularly in this line of work.

So, next time you’re crunching numbers for your Border Patrol entry exam or any related tasks, think about the incredible power of teamwork. You know what? Whether in the field or in the classroom, collaboration can turn a long, lonely task into a shorter, engaging exercise with a partner. Remember, it’s all about working together to reach your goals!

Let’s embrace the methods and strategies that help us nail those tricky problems as we gear up for success.