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Expert: - 11/6/2011


Question
1) A large pipe and a small pipe are used to fill a tank and a third pipe is used to drain the tank. If the three pipes are open, it takes 3 hours to fill the tank. If the large pipe and the drain are open and the small pipe is closed, it takes 6 hours to fill the tank. If the small pipe and the drain are open and the large pipe is closed, it takes 12 hours to fill the tank.  How long will it take each pipe to fill the tank alone if the drain is closed and how long will it take the drain to empty a full tank?

2) On a store counter, there was a supply of three sizes of Christmas cards. The large cards cost $25 each; the medium cards cost $20 each and the small cards cost $10 each. A woman purchased eighteen cards, which consisted of one fifth of the available large card, one third of the available medium cards and one fourth of the available small cards. The total cost of her cards was $295. If there were 50 cards remaining on the counter after her purchase, how many each kind of card did she buy?

Answer
1) Let's say the tank takes 36 globs of liquid (who knows how much a glob is,
but each glob is the same amount as another glob).

If all three are going, it takes 3 hours.
If the large income and outgo are going, it takes 6 hours.
If the small income and outgo are going, it takes 12 hours.

This means if all 3 are in use, there are 36/3 = 12 globs per hour incoming.
If the large and the outgoing are in use, there are 36/6 = 6 globs per hour.
If the small and the outgoing are in use, there are 36/12 = 3 globs per hour.

We don't know how much is going out yet, but lets say it is x globs per hour.
We know that if the small and large are both used, they should add up.
Taking the amount of globs in one hour, we get 12-x = 6-x + 3-x.

That is the same as 12-x = 9-2x, so 3 = -x, so the outgo adds x = -3 globs per hours.
In this way, with no outflow going on, the large inputs 6+3 = 9 globs per hour,
the small inputs 3+3 = 6 globs per hour, and together that is 9+6 = 12+3 = 15 per hour.

With a loss of 3 globs per hour, that is 3*15 - 3*3 = 45 - 9 = 36 globs, which checks out.

Since I called the tanks 36 globs, that makes it take 4 hours to fill for the large alone,
6 hours to fill for the small, and 12 hours for the drain to drain it all out.


2) I started with 12 of the 1st card and 1 of the 2nd, and kept decreasing the first and increasing the 2nd to the max; after that, I decreased the 2nd by 3 and increased the 3rd by 2.
Eventually I got to 1, 5, and 12.  The total number 1+5+12=18.  The number left is
4*1 +2*5 + 3*12 = 3+10+36 = 50.  The total price was 25x + 20y + 10z = 245.
This meets the conditions.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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