Mastering Combined Work Questions: Your Guide to GMAT Success

For combined work questions involving two workers, what is the formula for total time?

• A. T = (A + B)/AB
• B. T = (AB)/(A + B)
• C. T = (A + B)/A
• D. T = AB/(A - B)

Answer: (B)

The formula for total time when two workers are combining their efforts is derived from their individual work rates. If we denote the time it takes for the first worker to complete a task as A and the time it takes for the second worker as B, their rates of work can be expressed as follows: the first worker completes \( \frac{1}{A} \) of the task per hour, while the second worker completes \( \frac{1}{B} \) of the task per hour. When working together, their combined work rate is the sum of their individual rates, which is expressed as: \[ \text{Combined Rate} = \frac{1}{A} + \frac{1}{B} = \frac{B + A}{AB} \] To find the total time (T) taken for the two workers to finish one entire task together, we take the reciprocal of their combined rate: \[ T = \frac{1}{\text{Combined Rate}} = \frac{1}{\left( \frac{B + A}{AB} \right)} = \frac{AB}{A + B} \] Thus, option B, which states that total time \( T = \frac{

When it comes to the GMAT, nothing gets quite as tricky—or as rewarding—as combined work questions. You know what I’m talking about, right? Those questions where two (or more) workers are chipping away at a task together? Sure, it sounds simple at first glance, but these little problems can throw quite the curveball during your study sessions or on test day.

So, let’s break things down, shall we? The main question often revolves around finding the total time (T) it takes for two workers to complete a task when they’re working together. Now, here’s the kicker: instead of guessing what's happening in this scenario, we’ve got a formula that keeps everything nice and neat. Ever heard of it? Well, the game-changer here is:

[

T = \frac{AB}{A + B}

]

But first, let me explain what A and B represent. You see, (A) is the time taken by the first worker to finish a task alone, and (B) is the time taken by the second worker to do the same. Think of it like this: if one person can read a book in 4 hours and another in 6 hours, how long would it take them to read the same book together? Stick around, and I'll show you how to tackle it!

Now, when two individuals start working on a project simultaneously, their combined work rate is something magical—it’s the sum of their individual work rates! For instance:

[

\text{Combined Rate} = \frac{1}{A} + \frac{1}{B}

]

Pretty neat, huh? In our example, one worker reads ( \frac{1}{4} ) of the book per hour, while the other reads ( \frac{1}{6} ) of it per hour. If you add those rates up, you’re figuring out how fast they can accomplish the task together.

To put it simply:

[

\text{Combined Rate} = \frac{B + A}{AB}

]

Here’s where it all ties together. To find our total time (T) for two workers working side-by-side, we take the reciprocal of their combined rate:

[

T = \frac{1}{\left( \frac{B + A}{AB} \right)} = \frac{AB}{A + B}

]

That’s the brilliance of mathematical collaboration! No need to stress, right? Just plug in your values for (A) and (B), do a little math magic, and voilà—you’ve got your answer!

But wait, I can hear you asking, “What if one worker is slower than the other?” Great question! This is where understanding the formula becomes crucial. If (A) is larger than (B), it simply means that the first worker takes longer. But remember, teamwork can help balance that out.

And it’s not just about formulas; it’s about strategy, too. Some GMAT test-takers find these questions daunting, but why not mix and match the approaches? Practice using different variables or create mini-problems for yourself. It’s all about building your confidence.

Looking for additional strategies? Try timing how long it takes you to solve a couple of these questions, or even better—practice with a study buddy! When two minds work together, the topics become clearer, and your spirits lift. Talk about teamwork!

Beyond numbers, this is also a metaphor for life! It’s a reminder that collaboration often leads to better outcomes, and isn’t that true in many aspects? From group projects in class to workplace collaborations, knowing how to combine efforts effectively is a skill that pays off!

So, whether you’re facing two or three workers or even more complex scenarios, remember: keep practicing, stay curious, and lean on that teamwork mindset. Aim for balance, polish those problem-solving skills, and watch as those combined work questions turn from a source of anxiety into a badge of honor on your GMAT journey.