1. A 120 gallon tub has a drain which, when open, drains water at a rate of 6 gallons per minute. If the tub is empty and the drain is open, then at what rate, in gallons of water per minute, must water be added to the tub so that it fills in exactly 1 hour?
2. faster way of solving this problem?
I hope you have an answer book to check if I'm right, but I think it's all in how you think about it. If you need 120 gallons to fill the tub in 60 minutes, that is 2 gallons per minute. But it drains 6 gallons per minute, so you need to put in 8 gallons per minute. 6 will drain, and you will be left with 2 per minute adding to 120 in an hour.
2^21/ ((4^4(4^4 + 4^5)) =
The easiest way to do this one is to play around with the numbers to get the bases to 2. For instance 4^4 is really 2^8. So you can divide 2^21/2^8(4^4 + 4^5). Subtract exponents when you divide and you are left with 2^13/(4^4+4^5). The next step is a little tricky. You have to recognize that 4^5 equals 4^4 x 4. Then you can factor out 4^4. So you would have 2^13/4^4(1+4), which equals 2^13/2^8(5) which equals 2^5/5. or 32/5.
3. X^3YZ^2/ (X^6Y^4Z^6)^1/3 =
Another law of exponents. When you multiply exponents with the same base, you add the exponents. When you raise them to some power, you multiply the exponents. So that is really
X^3YZ^2/(X^2Y^(1/3)Z^2)
Since you are dividing you subtract exponents and Z^2 cancels.
X Y^(2/3) is about as far as you can break it down. It''s hard to read without superscripts though, so I may have made a mistake.
I hope that helps. The real key to the math section is speed. If you see a problem like these and you feel yourself wanting to work it all out the long way, DONT DO IT. They are there to stop you from having time to get 10 easy ones at the end. If you know how to do it, great. If you don't, make sure you get through the test first. Then you may have time to come back.
Please check the answers I gave you to make sure I'm right. If they are not, I'm sure I did something stupid that you can find.
