See if you can crack this problem in less than 2 minutes.

Ready, set, go!

*Mike paints a fence in 9 hours*

* Marty can paint the same fence in 5 hours*

**Column A**

The time it takes Mike and Marty,

working at a constant rate, to

paint the fence

**Column B**

3 hours

Work rates are one of my favorite problems to teach. Students usually have a formula in their heads that they vaguely remember. Even if they know the formula, they take awhile to put the numbers in the correct places. Assuming they don’t make a mistake, the problem can take them 2 minutes to finish.

What if I could show you a way to finish the problem in less than 15 seconds?

And that’s with no messy formulas.

Okay first things first let’s conceptually work through the problem.

Ask yourself, how much of the job does each person finish in one hour. With Mike, he finishes 1/9 of the job in one hour, because it takes him 9 hours to finish the entire job. With Marty he finishes 1/5 of the job in one hour. Add those two rates together, 1/9 + 1/5 = 14/45 and then Flip It! and you get 45/14. That is greater than 3, so the answer is (A).

Not bad. No cumbersome x and y, or Work Rate 1 and Work Rate 2, Total Work Rate, as many books on the market show you.

But imagine an even faster way. Ready?

All you have to do is multiple the hourly rate to find the numerator and add the rates to find the denominator.

Or more succinctly put, multiply the top; add the bottom.

9 x 5 = 45, 9 + 5 = 14. 45/14.

It’s that easy.

Let’s try two new numbers.

Mike = 15 hrs, John 5 hrs.

Now here’s all you have to do: multiply the top; add the bottom. In other words, multiply the time it takes Mike to do the job by the time it takes John to do the job. Then divide that by the sum of the time it takes Mike to do the job and the time it takes John to do the job.

(15 x 5)/(15 + 5) = 75/20 = 3 ¾ hrs.

Because it’s so easy try the next numbers:

7 hrs and 4hrs, Combined work rate: (Don’t look below till you’ve solved it)

**Ans: 28/11 hrs.**

I told you—no need to get “worked” up!

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This trick can also be use to add fractions by skipping LCM part . I developed this method in school and have saved lots of time since then especially if fractions have 1 in the numerator

like if you have to add 1/6+ 1/8 then, normally you would take 24 as the lcm and multiply the numerators with appropriate numbers and then add and so on

from thr trick its [8+6]/[8*6]= 14/48= 7/24

Hey, what trick trick do you have if you need add fractions like 7/9 and 8/9

This may be an instance where the basic operation is so easy that you don’t need a trick. With the denominators being the same, all you really need to do is add the numerators. 7 + 8 = 15, so 7/9 + 8/9 = 15/9. Then you can simplify as needed, creating either a whole fraction (5/3) or a mixed numeral (1 and 2/3).

Hey Chris

That’s awesome trick

You are genius buddy!!

You are welcome 🙂

Hey Chris,

While no doubt that this trick is AWESOME and a real time saver… the wording in the blog is misleading when you say, “All you have to do is multiple the hourly rate to find the numerator and add the rates to find the denominator.”

The correct way to phrase this in a formulaic manner would be:

Let Ta be the time A takes to finish the job while working alone,

Let Tb be the time B takes to finish the job while working alone and

Let Tab be the time take to finish the job when both A and B work together.

The correct formula is:

Tab = (Ta x Tb) / (Ta + Tb)

Yes, thanks for catching that! I meant to say “multiply the time A takes to finish the job…” Not “hourly rate”.

I’ll correct that in the blog 🙂

Hi Chris,

Just going back to what Karan pointed out or mentioned, and you also highlighted, you may want to correct the wording in this blog post above meaning: Multiply the time A takes to finish the job by time B takes to finish the job, and divide product by sum of time A takes to finish the job and B takes to finish the job.

This really is brilliant and saves a lot of time.

Cheers,

Samy

Great! Thanks for the feedback. Made some changes 🙂

This is awesome trick !!! Thank you Chris 🙂

You are welcome!

Chris,

You are really really great! thanks for posting such easy tricks 🙂

You are welcome!

This is one of the best methods/ ideas i have seen in the entire package. Saves me so much time doing these problems and anxiety. Thank you! I wish you could give tips like this for all the lessons instead of remembering formula after formula.

Great, I’m happy the trick made life easier :).

Sadly, there aren’t too many concepts that can be broken down this easily. I’ve a shortcut for combinations/permutations, some for rates and weighted averages, but otherwise there aren’t too many.

Chris,

You are the math teacher I wish I had in high school!! I am an old lady (45) going back to grad school after having kids, etc. It has been forever since I took math. You are making it possible for me to do this type of thinking again!!! Thank you so much

You are welcome! Thanks for the kudos and good luck :).

OMG! Cant believe you made it that easy……..not even 15 seconds, it just takes less than 5 seconds to solve the answer

awesome chris!!!! one question i am subscribed with magoosh material …… I want to know when and where can we use this flip technique!!! and in which kind of rate problems can we use the techniwue suggested by you as its a huge time saver and provides better understnding!!1

Hi Siddarth,

The “flip method” can only be used for work rate problems that give two differing rates. You might see one of these questions per GRE test. So definitely great as a time-saver, but limited in the type of problem you can use it on.

Hope that helps!

Thnxx Chris 😀 !!

Hi Chris,

I’m big fan of yours..the way you make things possible is tremendous I don’t even have the words..I’m preparing for gre and I follow everything you write with care…I don’t know how well I’ll do but you’ll always be my hero…

Thanks a lot for your work and thanks to the team behind magoosh

Wow, thanks for the kind words :). I’m so happy I am been helpful thus far. Good luck with your test and let me know whenever you have any questions :).

I usually never comment on these types of websites. But this lesson absolutely blew my mind. Thank you very much; all of your advice is great.

You are welcome!

Same here Chris! Blew my mind… this literally takes 10 seconds to answer a problem using this technique.

That was really great!

I am happy that helped!

You are my hero. Wow. Thank you!

Glad I could help! Thanks so much!!

Wow! Thanks Chris! I just can’t wait for the new GRE material to come out tomorrow!

Yep, Magoosh’s new GRE product is here! Also feel free to recommend any possible blog topics if there is a type of question/concept – math or verbal – that you find especially tricky while going through the new questions. Good luck!