# Brainteaser Answers – Issue 28,2014

In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 28, 2014 of the Automation Notebook. The brainteaser questions are repeated the answers are posted below each question. You can view the brainteasers from Issue 28, 2014 without the answers here: http://library.automationdirect.com/brainteasers-issue-28-2014

## Cavity Fighter

The miserly owner of the candy factory purchased 1000 gallons of molasses to fill his main storage tank. But because he was a cheapskate and didn’t spend any money on maintenance, the ancient valve at the bottom of the tank began leaking in the middle of the night. The following morning the factory workers arrived to find a huge mess with molasses all over the floor. The owner instructed the foreman to top off the tank with water, and to turn on the mixing apparatus in the tank to combine the water with the remaining molasses. The following night, the exact same amount of the new molasses/water mixture leaked onto the floor. Again the owner instructed the foreman to top off the tank with water and mix the solution. The factory’s chemist then ran a test and determined that the tank now held a mixture of 50% water and 50% molasses. How much of the contents leaked from the tank each night?

Answer:  The size of the spill is 292.9 gallons each night.

Hint: if you are thinking 250 gallons each night – please note that on the second night the leaked fluid includes a mixture of molasses and water.  Simply adding 250 gallons of water each morning would not result in 50% water in the tank.

Explanation:

Let x be the amount of lost product each night, we can express the amount of molasses lost each night as a percentage of the previous amount:  (1000-x)/1000

And we know that the final amount of molasses is 500 gals, but also that it is equal to  1000 gallons times the percent lost the first night times the percent lost the second night (the percents are the same).

So we can form the equation: 500=1000*((1000-x)/1000)*((1000-x)/1000)

Simplify to: X2-2000x+5000 =0  and use the quadratic formula to solve; x=292.89 Gallons

## Cellular Degeneration

The eccentric director of operations at the puzzle factory has fenced-off four identically shaped ‘work cells’ that completely fill the factory floor. The edges of the work cells fall on the grid pattern shown, and each work cell contains one pneumatically powered machine that uses NITRA™ components and one electrically powered machine that uses IronHorse™ Motors. Can you determine the shape of the work cells?