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An easier approach to Work/ Rate problems

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Manager
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Joined: 03 Jul 2017
Posts: 68
Location: India
Concentration: Finance, Economics
GPA: 3.4
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An easier approach to Work/ Rate problems  [#permalink]

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New post 07 Nov 2017, 12:12
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One of the most common areas on GMAT Quant is work and rate problems. I initially paid very little attention to them and realized these problems cost me a lot of time. One of the main reasons why these problems took me so much time was primarily because most of them dealt with fractions. Hence, I found an easier approach to tackle mostly all of these problems: visualize.

In order to visualize these problems, we are going to use a rate pie, which pretty much looks like this:
Image

The rate pie is a highly useful tool because whenever we have two pieces of the pie, we can solve for the third. Therefore, this makes it an especially useful tool when thinking about data sufficiency questions. As soon as we have two elements of three, we can answer the question.

Work = Time * Rate
Time = Work/ Rate
Rate = Work/ Time

And here's another good news! The only pre-requisite knowledge you require is simple multiplication and division along with some smart number picking techniques.

So here's an example:
Working alone, Mary can pave a driveway in 8 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 33.33%, but Hillary becomes distracted and her rate decreases by 50%. If they both work together, how many hours will it take to pave the driveway?

    A. 3 hours
    B. 4 hours
    C. 5 hours
    D. 6 hours
    E. 7 hours

Now, the question might seem intimidating at first, with rates and percentages and hours, so let's start with breaking it down.

To make this problem easier, we are going to assume the total work to be 48. Let's start by drawing the rate pie for Mary:
Image

As it can be seen above, it makes it incredibly easy for us to derive the rate for Mary, which is 6 units.

Now let's draw another rate pie for Hilary (note: the total work done remains constant):
Image

Once again, we can easily derive Hilary's rate, which is 8 units.

Now, the question tells us that working together, Mary's rate increases by 33.33% or 1/3 and Hilary's rate decreases by 50% or halves.
We can easily calculate
Mary's New Rate = 6 * 1 1/3 = 8
Hilary's New Rate = 8 * 1/2 = 4

We can now simply add these rates together to get a combined rate of 12.
Now we know, the total work and the rate. With one element to find, we use the rate pie:

Together (Mary + Hilary)
Image

The answer is B) 4 hours

Similarly, the concept of Rate Pie can be easily applied to any work/ rate problem and although it may seem time-consuming at first, once you get used to it, it saves a lot of time instead with increased accuracy.

This is one of my first attempts to explain a concept here on GMAT Club and I hope you found this post helpful.
Intern
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Joined: 15 Jan 2019
Posts: 1
Re: An easier approach to Work/ Rate problems  [#permalink]

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New post 17 Mar 2019, 23:26
Very nice tip. I was finding work rate problems always confusing

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Re: An easier approach to Work/ Rate problems   [#permalink] 17 Mar 2019, 23:26
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An easier approach to Work/ Rate problems

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