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Question
QUESTION: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, how many minutes would it take the slower pipe to fill the tank itself?
ANSWER: One pipe takes x minutes to fill the tank.
The other pipe takes x/3 minutes to fill the tank.
If 36 is split into 4 parts, the 1st pipe would fill 1 part and the 2nd pipe would fill the rest.
This means that in 36 minutes, the 1st pipe would only have 1/4 of the tank filled.
To fill the other 3/4 would take 3 times as long as it took to fill the first 1/4.
This means that it would take the slower tank 3(36) additional minutes, which is 108 minutes.
The first fourth took 36, and the last 3/4 took 108, so that answer is 36+108 = 144.
---------- FOLLOW-UP ----------
QUESTION: Scott,
The problem gives two polynomials p and q and I am asked to find the greatest common factor.
p(x)= x^4+2x^3+6x^2+8x+8
q(x)= x^4+2x^3+8x^2+8x=16
The greatest common factor (i.e.. the one of the highest degree) of p and q is______.
The question states with this knowledge of finding p and q, I should be able to simplify the ratio
p(x)/q(x)= (_______) / (___________).
I am at a loss of what to do, please help.
Thanks,
Ron
I assume that it is suppose to be q(x)= x^4+2x^3+8x^2+8x+16 (I believe the = should be a +).
I looked at both polynomials, and neither and has a 0.
x p(x) q(x)
-10 8528 8736
-9 5525 5695
-8 3400 3536
-7 1961 2067
-6 1040 1120
-5 493 551
-4 200 240
-3 65 91
-2 16 32
-1 5 15
0 8 16
1 25 35
2 80 96
3 221 247
4 520 560
5 1073 1131
6 2000 2080
7 3445 3551
8 5576 5712
9 8585 8755
10 12688 12896
Knowing this, neither of the polynomials will factor.
Since neither one factors, there is no way to cancel a term in either one.
You could say that it is 1 - 8/q(x), but I can see that answer is suppose to be in one fraction.
I managed to find time to do this, but won't be back until Monday.
I would say the answer is just p(x)/q(x).
I managed to squeeze in this answer, but I won't be able to do so again until Monday.
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Answers by Expert:
Scott A Wilson
Expertise
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?
Experience
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.
Publications
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.
Education/Credentials
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.
Awards and Honors
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.
Past/Present Clients
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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