Looking for a little help prepping for the SAT Math section?
In this video, Magoosh’s SAT expert Chris introduces the Work Formula and goes over several SAT practice questions to help you get comfortable with using the Work Formula on your own.
Watch the embedded video below, or scroll down for a full video transcript. 🙂
What Will I See in the “SAT Math Section: Work Formula | SAT Practice Questions” Video?
In this 9-minute video, Magoosh’s SAT expert Chris will take you, step-by-step, through three SAT practice questions, explaining how you can identify whether a question calls for the Work Formula and how to use the formula to solve even the hardest Work Formula problems!
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“SAT Math Section: Work Formula | SAT Practice Questions” Full Transcript
Hi, I’m Chris, the SAT expert at Magoosh, and for over 15 years I’ve been helping students ace the SAT.
And today we’re gonna talk about the work-rate formula.
So what’s cool about the work-rate formula is it deals with a question type that if you didn’t know the formula you’d be pretty much stuck and have no idea what to do.
And that’s why this formula’s so great.
It’s really simple, and it unlocks a tough kind of question type.
And so, I’m gonna teach you a formula called the FAF formula, for Flip, Add, and then Flip.
And this is gonna make everything so much easier.
So here it is.
That set up I was talking about.
Machine A takes 4 hours to finish the job and machine B takes 3 hours to finish the job.
Working together, how long does it take them to finish the job?
So I know I’m dealing with work rate because we have the rates here, the number of hours, 4 hours and 3 hours, and we also have this word here, working together, so we can see wer’re combining those rates.
Now, you can’t just add these together and say, oh, 4 hours plus 3 hours, that would take them seven hours to finish the job together.
Because they are actually working together, so they’re gonna do the job faster than they would just working alone.
Would you take the average of it?
Well, no, you wouldn’t add 4 plus 3 into 5 by 2, because even that is a little bit slower.
That would be 3.5 and that would be a little bit slower than the 3 hours that one takes the job to finish the job by themselves.
And again, we know that, if they’re working together, they do it faster.
So if we just sit here all day thinking about this intuitively, it’s gonna be really hard.
And you obviously don’t have time on the test.
And that’s why I’m gonna show you a simple technique to deal with these kinda questions.
And it is called the FAF Method for Flip, Add, and Flip.
Let’s see how this actually plays out because you might be wondering, what do you mean by flip.
So let’s check it out.
Pick the first rate here which you see which is 4 hours.
Now, you can think of that as just the number 4 and when I say flip it over, what I mean is the reciprocal.
So the reciprocal of 4 is 1/4.
Okay, next step.
You wanna add the 1/4 plus the 1/3.
You might be thinking, whoa wait a second, where did you get 1/3 from?
Well the idea is, we wanna add up the reciprocals of both their rates.
And so 4 hours corresponds here to 1/4 for the first machine and for machine B we want to flip and do the same thing so that we get 1 over 3, that is, we flip 3 and get the reciprocal which is 1/3.
At that point, once I’ve done that with both traits then I can add them up together.
And then this gives me 7 over 12.
I know, that was super fast, how did I do that?
Cool method you might not have learnt this in school but if you have two fractions and you’re adding them up together.
And both of them have one in the numerator, all you need to do is take the denominator, both numbers in the denominator, in this case 4 and 3, and add those together.
4 plus 3 is 7.
And then put that in the numerator, put a line as I did here.
And then for the denominator, just do 4 times 3, which is 12, 7 over 12.
That’s a little side show here though because we’re focusing on the FAF method.
And now we need to go to the final step which is to flip.
So just a second ago I added up 7 over 12, what do I do?
I take the reciprocal of that, that’s why we have the double flip there.
First flip here, second flip there.
So 7/12 the reciprocal of that is 12/7ths, which is 1 hour and 5/7th or 1 5/7th of an hour or just 12/7 an hour.
If this were a multiple choice test, they would probably leave it in this form and that would be the answer.
Okay, so now that we’ve seen that, that we take both rates, we flip them, and then we add the reciprocals here, second step.
And once we’ve added the reciprocals, we flip again to get the answer.
So let’s try that out here in the next slide.
This one has Deborah.
And if you wanna be bold and try it at home by yourself, pause and see what answer you’ll get and watch and wait to see what answer I get.
Hopefully they match up.
Okay, if you did possibly try this at home or if you didn’t doesn’t matter, cuz I am heading on now so here we go.
Deborah takes 2.5 hours to paint a fence.
Her friend Molly takes 2 hours.
How long it will take them to paint the fence if they work together continuously?
There again it is, the work rate, both doing it.
We need to combine it, we need to flip, right?
FAF, so what’s the first thing we do?
Well, we take the first rate which is 2.5 hours and you might think oh, I get it, this is great, 1 over 2.5.
And then you’re gonna be ah, what happened here.
Well that’s what can easily happen and the test writers know that, and that’s why they try to throw students off by putting decimals in there, but you should know that 2.5 is the same as two and a half.
You should also know that two and a half could be written as five over two
That’s great because what is the reciprocal of 5 over 2, well we can flip that very easily and get two fifths.
Then we add that to, what’s the next one?
Molly, Molly takes 2 hours.
The reciprocal of 2 is one halves, a lot easier.
We do the math here, we find out that 2 over a 5th is the same as 4 10ths so write that down.
And one-half is the same as 5 10ths.
Look at that, just like that we get to the answer, which is 9/10ths.
Or is it?
And that’s the tricky part it’s the FAF method.
Not the FAH method.
We always have to make sure to flip the final result here when we add them together so you flip 9 over 10 over here, you get 10 over 9.
So the answer is not less than one hour which you might have fallen for.
But it is between 1 and 1.5 hours cuz 10 over 9 is slightly more than 1.
And there we have it, that is the answer here.
Okay, we’re gonna try one more, and just as this one was a little bit harder than the first one, this last’s one gonna be even harder.
So if you didn’t get this, I would still encourage you to try this at home.
Of course if you did answer the question with Deborah and her friend painting the fence, then definitely try this.
Pause the video and then you can have a look.
Okay, unpause the video and here we go.
A pump working at a continuous rate can empty a full pool in 9 hours.
A second pump working at a continuous rate can completely fill an empty pool in 6 hours.
Okay, let’s stop there.
That already is quite a headache, my head is spinning, what’s happening?
And that’s fine, you could reread it again slowly, digest each part.
Notice that the first pump is defined in terms of how it empties a pool, so it’s actually sucking water out of the pool, and it takes 9 hours to do so.
The second pump is filling the pool, so it’s adding water.
So you’re having this counter effect here.
So what do we do there?
Let’s stop there.
We have 9 hours on the first one, we can take the reciprocal there, we know, our FAF, that’s 1/9th with the emptying of the pool.
And then with the filling of the pool, we can get 1 over 6.
Again, I’m taking the reciprocal of 6 hours.
Now I’m going to write it there next to it.
Now my question is, are we adding these rates together?
Because the FAF is Flip, Add, and Flip, and that is most of the times the problems you will get.
And so if you did this and you would think, hey, I don’t think FAF really works, in a way you’re right.
We have to change it to FSF or Flip, Subtract, Flip, but that doesn’t roll off the tongue, obviously.
But the point here is the concept is the same, though.
Instead of adding these numbers, we are going to subtract them.
Why, because, again, one of the pumps is filling up the pool.
The other one is working against it, right?
Emptying the pool, and that’s why we’re subtracting them.
And so we have 1/6 minus 1/9 because the one filling that, that’s gonna give us the water, is the first one, 1/6 and the one emptying the pool taking water away, that’s why we’re subtracting it as 1/9.
And so we use this method and now we’re subtracting, we get 3 over 18 minus 2 over 18 on this side and that gives us 1 over 18 and that’s great.
Well, what is 1 over 18 then?
1 over 18 is how much the pool fills in one hour.
But what’s the final step now?
Now we go back to the FAF part, you flip it over and you can see that, okay, in this setup, it would take 18 hours to fill.
Again, a long time, but you have one pump that’s sucking water out, while the other one is filling the pool up with water.
So, that’s 18 hours worth.
So, is that our answer?
D, it’s screaming at me.
Well, we never did read the end of the question which is, if a pool is half filled with water, how long would it take the pool to fill completely then?
Now what was that part that I just read?
That important part, it is already half filled with water.
So you don’t need to have all 18 hours there.
You can see it’s already half filled up so you’re only going to need 9 hours worth.
Because in 9 hours, the set up here with these two pumps, in 9 hours they fill up half the pool, and so therefore C is our answer.
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And I will see you next time.
Want More SAT Study Tips?
Take a look at some of our other useful study tips to help you prepare for the SAT Math section:
- Tips to CRUSH the SAT Math Section | Video Post
- SAT Math Practice: How to Study Smarter and Score Higher
- 5 SAT Math Tricks Every Student Should Know
Happy studying! 🙂