CHAPTER 7
ADVANCED CONCEPTS
In many problems, it is necessary to use complex word combinations to express an idea or dimension.
We have already discussed the concept of ‘ft. x ft.’ to express the area of a room as ‘square feet’.
Sometimes, two different words need to be multiplied together to show the idea. One common example of this is:
KILOWATT HOUR
What exactly does this mean ? The word ‘Kilowatt’ means ‘1,000 watts’ (‘Kilo’ is a metric system term
for ‘1,000’). Fine ! Where does the word ‘hour’ come in ?
A ‘watt’ is an electrical term for ‘power’. When you buy a ‘100 watt’ lamp, the ‘100’ indicates how much
power is required to operate it. But power is not the only consideration ! ......
If your neighbor operates HIS lamp bulb all night while you only operate your for 3 hours, the
electric company will charge him more. Why ?
Because the electric company's rates are based upon "ENERGY" not "POWER" ! Thus, we need a
'word phrase' for "ENERGY". Do you remember Rule 12 ? (Re-read it)
KILOWATT HOUR = KILOWATT x HOUR
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Another concept that is confusing to many (including college graduates) is the concept of
‘interest on a loan’.
RULE # 52 INTEREST IS THE AMOUNT MONEY A LENDER CHARGES A BORROWER FOR
USING THE LENDER’S MONEY. INTEREST CHARGED IS DEPENDENT UPON :
AMOUNT, LENGTH OF TIME IT WAS HELD AND RATE OF INTEREST.
Most adults understand Rule #52 in a general sense. However, the key phrase which causes confusion
is ‘length of time it was held’. The word ‘it’ obviously refers to the amount of money borrowed.
(This is called: ‘principal’ ). If you borrowed $ 100 for a year, this means that you (the borrower)
should keep the entire $100 principal for a full year !
If you repay any part of the principal during the year, then that would not be true !
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Another important concept can be called ‘parallel jobs’. ‘Parallel’ means ‘side-by-side’; ‘parallel jobs’
refers to two or more things doing the same job at the same time, each contributing a portion towards
completing the overall job.
For example, filling a swimming pool with two water hoses. If each hose were the same size, we would
correctly guess that both hoses could fill the pool in half the time it would take a single hose to fill it by itself.
What if the hoses were not the same size (diameter) ?
===================================================================================================================
Click for answers PROBLEMS
1. The electric company charges $0.03 per kilowatt hour. What will it cost to operate 15 lamps
(60 watts each) for 10 hours and 5 hair dryers (200 watts each) for 2 hours ?
2. A man borrowed $2000 from a bank. Four(4) months later, he repaid the bank $2100
(including interest charge). What is the true annual interest rate he was charged?
3. The earth has a circumference of 25,000 miles. If the circumference increased to 25,001 miles,
by how many yards would the radius increase ?
4. Two brick layers can build a house in 30 days. If the first can build it himself in 45 days,
how long would it take the second to build it alone ?
BONUS QUESTION: THIS IS NOT A BRAIN TEASER OR PUZZLER. IT CAN BE SOLVED BY
DEVELOPING A RELATIVELY SIMPLE EQUATION !
Joe is 24 years old. Joe is twice as old as Bill was when Joe was as old as Bill is.
How old is Bill ?
ADVANCED CONCEPTS
In many problems, it is necessary to use complex word combinations to express an idea or dimension.
We have already discussed the concept of ‘ft. x ft.’ to express the area of a room as ‘square feet’.
Sometimes, two different words need to be multiplied together to show the idea. One common example of this is:
KILOWATT HOUR
What exactly does this mean ? The word ‘Kilowatt’ means ‘1,000 watts’ (‘Kilo’ is a metric system term
for ‘1,000’). Fine ! Where does the word ‘hour’ come in ?
A ‘watt’ is an electrical term for ‘power’. When you buy a ‘100 watt’ lamp, the ‘100’ indicates how much
power is required to operate it. But power is not the only consideration ! ......
If your neighbor operates HIS lamp bulb all night while you only operate your for 3 hours, the
electric company will charge him more. Why ?
Because the electric company's rates are based upon "ENERGY" not "POWER" ! Thus, we need a
'word phrase' for "ENERGY". Do you remember Rule 12 ? (Re-read it)
KILOWATT HOUR = KILOWATT x HOUR
-----------------------------------------------------------------------------------------------------------------------------
Another concept that is confusing to many (including college graduates) is the concept of
‘interest on a loan’.
RULE # 52 INTEREST IS THE AMOUNT MONEY A LENDER CHARGES A BORROWER FOR
USING THE LENDER’S MONEY. INTEREST CHARGED IS DEPENDENT UPON :
AMOUNT, LENGTH OF TIME IT WAS HELD AND RATE OF INTEREST.
Most adults understand Rule #52 in a general sense. However, the key phrase which causes confusion
is ‘length of time it was held’. The word ‘it’ obviously refers to the amount of money borrowed.
(This is called: ‘principal’ ). If you borrowed $ 100 for a year, this means that you (the borrower)
should keep the entire $100 principal for a full year !
If you repay any part of the principal during the year, then that would not be true !
--------------------------------------------------------------------------------------------------------
Another important concept can be called ‘parallel jobs’. ‘Parallel’ means ‘side-by-side’; ‘parallel jobs’
refers to two or more things doing the same job at the same time, each contributing a portion towards
completing the overall job.
For example, filling a swimming pool with two water hoses. If each hose were the same size, we would
correctly guess that both hoses could fill the pool in half the time it would take a single hose to fill it by itself.
What if the hoses were not the same size (diameter) ?
===================================================================================================================
Click for answers PROBLEMS
1. The electric company charges $0.03 per kilowatt hour. What will it cost to operate 15 lamps
(60 watts each) for 10 hours and 5 hair dryers (200 watts each) for 2 hours ?
2. A man borrowed $2000 from a bank. Four(4) months later, he repaid the bank $2100
(including interest charge). What is the true annual interest rate he was charged?
3. The earth has a circumference of 25,000 miles. If the circumference increased to 25,001 miles,
by how many yards would the radius increase ?
4. Two brick layers can build a house in 30 days. If the first can build it himself in 45 days,
how long would it take the second to build it alone ?
BONUS QUESTION: THIS IS NOT A BRAIN TEASER OR PUZZLER. IT CAN BE SOLVED BY
DEVELOPING A RELATIVELY SIMPLE EQUATION !
Joe is 24 years old. Joe is twice as old as Bill was when Joe was as old as Bill is.
How old is Bill ?
