*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.

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?

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.

**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!)**

- If there are 3 or more people involved, is the formula still applicable?
- 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**

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. 😛*

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