Short Cut #3: Wacks Work Formula (a.k.a. MOA)

by Wacks Formula

 

This is probably my oldest short cut in my shelf — a real time-saver in exams and will help you solve algebra without learning algebra.  (If only everything in life is like that.)

A common algebra work problem:  Person 1 can do something in a given time.  Person 2 can do the same, different amount of time.  Question:  How much time if they work together?  Goes something like this:

 

Shanny can paint a house in 3 hours.  Yanny can paint a house in 6 hours.  If they work together, in how many hours will they finish painting a house?

 

Warning!  Don’t add, subtract of get the average of the given.  Send me a message (and some snacks) if you want to know why.

 

Picture1

 

Long Method:  Algebra! Yay!  (Don’t do this, unless required. After knowing the short cut later, please erase this part.)     

     

Let: 

a = time of person 1 (in this case a=3)

b = time of person 2 (in this case b=6)

x = time if they work together

First we translate time to rate. By definition, a person’s working rate = 1/time.  Therefore:

1/a = rate of person 1 (in this case 1/3)

1/b = rate of person 2 (in this case (1/6)

1/x = rate of person 1 and 2 together

Next place them side by side in this unintelligible equation:

1/a + 1/b = 1/x

This means rate of person 1 + rate of person 2 = rate of them together.  Plugging in values:

1/3 + 1/6 = 1/x

Solving using brute force algebra of fractions:

2/6 + 1/6 = 1/x

3/6 = 1/x

1/2 = 1/x

x = 2

Finally done after 17 lines. 🙂

 

Now presenting:

Short Cut #3:

WACKS WORK FORMULA  

(for Work Problems)

STEP 1.  Multiply the two given.

STEP 2.  Add the two given.

Step 3:  Divide the result.

 

Back to the example:

Shanny can paint a house in 3 hours.  Yanny can paint a house in 6 hours.  If they work together, in how many hours will they finish painting a house?

 

Picture2

 

STEP 1.  Multiply  –>  3 X 6 = 18.

STEP 2.  Add  –>  3 + 6 = 9.

STEP 3.  Divide the results –>  18 / 9 = 2

 

Answer:  2 hours

 

A useful mnemonic for the short cut is “multiply over add”, thus the other name MOA.

 

Picture3

 

NOW, TEST WHAT YOU HAVE LEARNED!

 

1.  Wei-Wei can eat a burger in 30 minutes.  Xhau-Xhau can eat a burger in 15 minutes.  If they eat together, in how many hours will they finish eating a burger?

2.  Pipe A can fill the Parkview swimming pool in 5 hours.  Pipe B can fill the pool in 20 hours.  If both pipes are open, how much time is needed to fill the pool?

3.  CHALLENGE:   Ming-Ming can erase the board in 12 seconds.  Jun-Jun can erase the board 3 times faster than Ming-Ming.  If they erase the board together, in how many seconds will they finish?

 

Deeper thoughts for the Pro (if you are BRAVE enough!)

  1. If there are 3 or more people involved, is the formula still applicable?
  2. What happens to the formula if the two tasks are opposite?  Example, one pipe is filling the pool and one pipe is draining the pool?

 

See you next episode! 🙂

 

–Wacks Formula

 

<<Previous

Short Cut #2: The Wacks Middle Finger Technique

 

Disclaimer:  

1.  The name of the formula is purely for fun, and does not discredit others who might have discovered the same formula independently.

2.  Names of characters used in the word problems are purely products of the author’s imagination.  Any resemblance to a real living person is just a coincidence. 😛

 

Advertisements

One thought on “Short Cut #3: Wacks Work Formula (a.k.a. MOA)

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s