Work Rate Problem Introduction &Challenges
Hi guys! Today we’re going to look at a super challenging work rate problem. This is one of those keystone problems, where if you have this problem really, really down then it indicates that you won’t have a problem with any work rate problem, speed-distance problem whatsoever.
The challenges in this problem are several. First off, you don’t have any base number to work with. That is, it’s all done in percentages and while a lot of times this can be an asset for running a scenario, here the scenario can really trip us up, as we’ll see. We also are being given different movements that are happening in different directions and it’s not entirely clear from the language in this problem that they are happening in different directions. Finally, there’s a notational issue that both the problem and the answer choices are in percentage and yet with work-rate, speed-distance, many times it’s best to work with fractions. So we have the option to notationally shift over to fractions and back. So let’s dive in.
Machine Efficiency (& Inverse)
On its surface, this is a textbook GMAT problem and what we’re being asked for is relatively straightforward. That is, there’s not a large interpretive part to understanding what we’re being asked for. The challenge here is how we’re going to get it. What would be the best way to approach this, in my opinion, for most people is to break apart the two different changes that are happening in the problem: the machine efficiency and the length of the production process and understand what each of these two tweaks is doing to your overall problem. Let’s begin with the production time.
The length of the production is decreasing by 25. So the pivot question is how much time is this saving us? And you’re right, it’s on the surface, it’s 25%. But we want to take the inverse of this because we don’t care about the time that it’s saving us, even though the question’s asking that. Rather, what we need to do is figure out how much total time we’re taking at the start versus with these tweaks and see how that’s affected so we’re going to have to invert everything and instead of saying: okay I’m saving 25% of my time, it’s taking only 75% of the time. If we do this in fractions we’re saving 1/4 so it takes us 3/4’s as long to do the same thing. Let’s take that three quarters put it to the side for a second.
The second part is a little more tricky! Our speed is increasing by 1/3 but that’s the inverse that is when we go faster the time we’re going to spend decreases. I’ll say that once more: the faster we’re going the less time we’re spending. So what does increasing our speed by a third do for us? Well instead of making 3 things, in the same amount of time we can make 4 things. We start out with a unit and we’re adding another third. Three parts, three, four parts.
So once again we are taking only 3/4s of the time to do the same thing due to the increased speed so we only have to spend 3/4s of the amount of time for the increased efficiency and only three quarters of the amount of time for the speed. We put those together multiplicatively and we find that it’s going to take us 9/16 of the time that we used to spend doing in order. The flip of that where we invert, is that we’re saving 7/16 of our time or a little under half. You’ll see from the answer choices that if you’re attuned, you’re limited to the 56.25% and/or 62.5%.
And if you’re familiar with your eighths being 50 and 62.5 as two of the of the eighths, then it’s got to be that 56 number. So there’s a bit of known numbers feeding into this but ultimately the challenge is doing these inversions and recognizing that these problems are built for fractions. Not just this one but just about every work-rate problem.
Deal With Work Rate Problems Fractionally
You want to deal with it fractionally because it’s these ratios of time, the numerator to the denominator that allow us to do things flexibly and to flip stuff around. 4/3s to 3/4s as we saw in this problem. Notice here that running a scenario, especially if you choose a generic number like: Okay well let’s say I make 100 widgets is going to get you into a ton of problems because it’s going to be extraordinarily complex from a calculation standpoint.
You can think about it in advance and choose really good numbers but in doing so you’ll have circumvented the solution path and logically push yourself into saying well wait this is going to be 16ths of something. So for just about everyone out there I would say put it into fractions think carefully and deeply about what each of these two switches does and then put it all together the way you would any other problem. Post your questions below. Subscribe to our channel! And come visit us anytime at www.apexgmat.com. I’ll look forward to seeing you guys again soon.
For another gmat work rate problem, try this Car Problem.