Ok, So I'm taking the SAT's in the morning, and I've been taking online practice tests. I'm fine on everything except for a certain kind of question from Algebra 1 (which i took 4 years ago). Can Anyone around here explain how to do this problem to me.
If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
2 minutes and 44 seconds
2 minutes and 58 seconds
3 minutes and 10 seconds
3 minutes and 26 seconds
4 minutes and 15 seconds
The answer is 2 minutes and 44 seconds, but i can for the life of me figure out how to get it...
Posted by ricree101 (Member # 7749) on :
figure out how many drinks each mixes in a given unit of time (drinks/second would be your best bet for this problem).
Then, once you know the rates, multiply them all by some time T to find out how many drinks are mixed during that time.
Then set the whole equation to 20 drinks.
You'll end up with
(R1 + R2 +R3)*T = 20;
Where R1 is Steven's rate, R2 is Sue's rate, adn R3 is Jack's rate.
Posted by El JT de Spang (Member # 7742) on :
Steven mixed drinks at a rate of 20drinks/5minutes = 4 dpm Sue mixes at 2 dpm Jack mixes at 1.3 dpm
Together they mix (4+2+1.3) = 7.3 dpm
7.3 drinks/min = 20 drinks/x min
Cross multiply and solve for x.
Posted by Miro (Member # 1178) on :
Stephen can mix 20 drinks in 5 minutes. So 20/5 = 4 drinks/minute.
Sue can mix 20 drinks in 10 minutes. So 20/10 = 2 drinks/minute.
Jack can mix 20 drinks in 15 minutes. So 20/15 = 1.33 drinks/minute.
4 + 2 + 1.33 = 7.33 drinks/minute
(20 drinks)/(7.33 drinks/minute) = 2.73 minutes
Multiply the decimal portion by 60 to get seconds, and you have your answer.
Good luck with the SATs. Posted by El JT de Spang (Member # 7742) on :
Ha ha, Miro! Too slow!
Or, great minds think alike.
Posted by Miro (Member # 1178) on :
Posted by ricree101 (Member # 7749) on :
One piece of advice for the math portion of the SATs: Don't worry too much if you think the answer is not enough information. You can always come back to the problem later, and if there really isn't enough information you could spend way too long on a given problem.
I say this because I barely finished half of the questions on the math section my first time taking the test.
Posted by MrSquicky (Member # 1802) on :
7 1/3 drinks/minute * X minutes = 20 drinks 20/7.3333 = 2.7 something, which translates to 2 minutes 44 seconds.
That's the long way. The easier way, the way you're supposed to do it, is to say 3 minutes gives you 12 + 6 + 4 = 22 drinks, thus it has to be the 2:44 answer.
Posted by J T Stryker (Member # 6300) on :
*light bulb goes on*
Wow... that really was easy... Thank you so much... I feel really silly for pondering over this for 45 min...
O-well...
I now feel confident in my ablilty to take this stupid test... You have no idea how stressed I am over it... I've got to get atleast a 2000 on it...
*disappears back into the darkness where lurkers dwell*
Posted by ricree101 (Member # 7749) on :
quote:Originally posted by El JT de Spang: Ha ha, Miro! Too slow!
Or, great minds think alike.
I could say the same to you. Posted by KidB (Member # 8821) on :
Make sure you get "Steven" to mix you a stiff one after the test. You'll need it.
Posted by ricree101 (Member # 7749) on :
quote:Originally posted by J T Stryker: *light bulb goes on*
I now feel confident in my ablilty to take this stupid test... You have no idea how stressed I am over it... I've got to get atleast a 2000 on it...
Did they change the scoring on the test?
Posted by El JT de Spang (Member # 7742) on :
Good luck on getting a perfect + 400 points. That would be impressive. But as Squick and ricree say, best to try to intuit what the answer ought to be than to actually pound through formulas on a timed test.
Do the easy ones first, then come back to the hard ones is my advice. That's what I did on the F.E.
Posted by J T Stryker (Member # 6300) on :
yes... they added another 800 points to the old system when they added the essay.
Posted by MrSquicky (Member # 1802) on :
2000? Did they change the SAT scoring?
JT, I got a perfect score on the SAT, I used to tutor for it, and two of the big pieces advice I can give you is 1) stressing over it is a really bad idea and 2) there are tricks, like the multiplying by 3 minutes (which is suggested by the only fractional proportion being 1/3 and the answers clustering around the 3) to many of the problems that make them much easier to solve. I don't know that the night before the test is the best time to think about that, but keep in mind when you're taking it that, if a problem seems very complicated, there's probably a silly little trick like that that will make it much easier. (Oh, and watch out for the pos/neg switch, especially when dealing with square (and any even power) roots and be on the look out for the things that work except when x = 0.)
Good luck.
Posted by J T Stryker (Member # 6300) on :
Thanks Mr.Squicky... I am trying my best not to stress over this stupid test, but i've been accepted into NYU pending my SAT scores... And NYU is my first choice for next year...
Posted by Miro (Member # 1178) on :
I can just imagine the abuse until people get used to it. "Yes sir, I got 1600 on my SATs."
Posted by MrSquicky (Member # 1802) on :
JT, If you don't get it this time, it's not the end of the world. You'll have at least one more chance to take it in the spring. Best advice I can give you is to stop thinking about the score you have to get. Put it out of your mind. You'll do much better on the test if you can do this. Strange as it may sound, taking the SAT can be kinda fun, if you approach it the right way. I was out at a party the night before I took em.
Posted by J T Stryker (Member # 6300) on :
True, but I would much rather not wait until next may to know where I'm going...
But I will do my best not to think about my score... I have to say, now that I can do simple algebra again, I feel a lot less stressed...
Ok, now i'm going to bed...
Thank you all...
Posted by Mr.Funny (Member # 4467) on :
They have a math section, a writing section, and a critical reading section. The essay contributes to the writing score. They basically split up the verbal section into two other sections. It's out of 2400 now. I'll be taking the SAT myself in the semi-near future. I'm hoping to score in the 2200+ range.
Posted by MrSquicky (Member # 1802) on :
Critical reading, eh? Do they still do the analogies and antonyms and such or is it all crit reading?
Posted by James Tiberius Kirk (Member # 2832) on :
No more analogies-- mostly passages now.
It's ten sections (Nine real sections and one ungraded "test" section).
Many schools ignore the writing section or count it as an SAT-II score. I personally hate the new format. My dad had me practicing for years, and they changed it on us
Good luck JT (and Mr.Funny). I'm taking the IIs tomorrow; hoping I do just as well on this one...
--j_k
Posted by Mike (Member # 55) on :
The answer is actually 3 minutes exactly. Not what they're looking for, I'm sure, but it's correct nevertheless. At 3 minutes, Steven has just finished mixing his 12th drink, Sue her 6th, and Jack his 4th. Which comes to 22 drinks total. But a second before the 3-minute mark only 19 drinks have been mixed. To get their answer you'd have to assume that three bartenders can work together exactly as efficiently as they would alone, a pretty dubious assumption. I'm actually surprised no else has pointed this out. *looks around the thread to make sure*
(And somehow I got a perfect score on my math SAT and not on my verbal. Hmm. )
Posted by J T Stryker (Member # 6300) on :
I think i'll have that stiff drink now Steven...
I think I did it....
Posted by lord trousers (Member # 8741) on :
quote:Originally posted by El JT de Spang: Steven mixed drinks at a rate of 20drinks/5minutes = 4 dpm Sue mixes at 2 dpm Jack mixes at 1.3 dpm
Together they mix (4+2+1.3) = 7.3 dpm
7.3 drinks/min = 20 drinks/x min
Cross multiply and solve for x.
The computer scientist in me says this answer is absolutely ridiculous, and indicative of the cloud of unreality that math professors usually walk around in.
20 drinks / 7.3 drinks/min = 2.739726027 minutes, or 2 minutes, 44.383561644 seconds. There are two problems with this answer, and the people making the SAT should be smarter than this.
First, if you round down, you'll get an answer that's too low. If you divide it back out - 20 / 2.733333333 - you get a combined rate of 7.317073171 drinks/min, which is faster than the combined drink-mixing rate of 7.3 drinks/min. They should round up instead.
Second - and worse - this assumes all three are capable of mixing the same drink at the same time without any reduction in efficiency. (Huh?) That's a really bad assumption, so let's take it out. In 2:44 minutes, Steven can mix 10.933333333 ~ 10 drinks. Sue can mix 5.466666666 ~ 5 drinks, and Jack can mix 3.553333333 ~ 3 dinks. 10 + 5 + 3 = 18 drinks.
(Assuming they can work on the same drink at the same time - totally infeasible, of course - Sue and Jack would mix one final drink together, and then both of them would help Steven with his last.)
Let's try having someone mix a non-fractional number of drinks and see what happens to the others.
Let's have Steven mix 11 drinks exactly. That's 11 / 4 = 2.75 minutes. Then Sue can mix 5.5 ~ 5 drinks, and Jack can mix 3.575 ~ 3 drinks. 11 + 5 + 3 = 19 drinks. Too short.
Okay, Sue's turn. She mixes 6 drinks: 6 / 2 = 3 minutes. Then Steven mixes 12 drinks, and Jack mixes 3.9 ~ 3 drinks. That's 6 + 12 + 3 = 21 drinks.
If Jack does 4 drinks, 4 / 1.3 = 3.076923077, which is larger than 3 - so that won't work either. We need an answer between 2.75 and 3.0 minutes.
Okay, that didn't work. Hey - one of the answers is 2.966666667 (2:58) minutes. Let's try it: Steven does 11.866666667 ~ 11, Sue does 5.933333333 ~ 5, and Jack does 3.856666667 ~ 3. 11 + 5 + 3 = 19 - whoops. I really thought they'd have it.
Well, it turns out this problem cannot be solved. Here's why: at 3.0 minutes, both Sue's and Steven's number of drinks roll over to an integer. At 3.0 minutes, they go from 19 drinks to 21 drinks.
Like I said, whoops. The SAT people really messed up on this one.
The worst thing is that people like me (both mathematical and incessantly pragmatic) would spend way too long on a problem like this to verify that they'd got it wrong. I'd finally put down 2:44 because that's what they were looking for.
I'd feel dirty, though. Posted by Mike (Member # 55) on :
Psst, lord trousers, look up two or three posts. Posted by lord trousers (Member # 8741) on :
Yeah, I saw that. You're wrong.
It's 21 drinks, not 22. Jack does 3.9 in 3 minutes.
Okay, so I saw it after I posted. So what? Posted by Mike (Member # 55) on :
There was a case many years back (though this story might be apocryphal) that there was an unintentional trick question on the math SAT that ended up being successfully appealed. The question was this: if you take a regular tetrahedron and regular octahedron whose faces have the same area and glue them together along one face, how many faces does the resulting figure have? The answer they were looking for, 8 + 4 - 2 = 10, is not correct. Don't believe me? Look here. (OK, so I skipped a few steps. Sue me. )
[Edited the link so it makes slightly more sense.]
Posted by Mike (Member # 55) on :
quote:It's 21 drinks, not 22. Jack does 3.9 in 3 minutes.
Nope. Check your rounding errors.
Posted by lord trousers (Member # 8741) on :
Gah! It was El JT de Spang's rounding errors!
That's the last time I use someone else's numbers. Jack's rate is 1.333333333 drinks/min, not 1.3.
Posted by Mike (Member # 55) on :
No worries.
Incidentally, if a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half?
Posted by breyerchic04 (Member # 6423) on :
Who are Sue and Steven, and when did Jack get so fast, I thought he had to drink them in between. Good job kid, I hope you can get as far away from this town as humanly possible.
Posted by J T Stryker (Member # 6300) on :
Amen...
Posted by theCrowsWife (Member # 8302) on :
The analogies were the best part of the SAT. I loved them.
--Mel
Er...where did starLisa's post go?
Posted by breyerchic04 (Member # 6423) on :
Yeah I thought that too!
Posted by Mr.Funny (Member # 4467) on :
quote:Originally posted by Mike: No worries.
Incidentally, if a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half?
I think that the answer is 20/21 hens. The original hen lays 1 egg every 1.5 days. Thus, better by a half would be 1 egg per day, so the new set of hens lays at 1 egg per day. A week and a half is 10.5 days. The number of eggs to be layed (laid?) is a half a score and a half, which is 15. Since it's "how many and a half", the many part will lay 2/3 of the total eggs, or 10 eggs. Thus, the many portion will lay 10 eggs in 10.5 days. This must mean that there are 20/21 of a hen for the "many" portion, since the hens lay at 1 egg/day.
Posted by Mike (Member # 55) on :
I think the way it's supposed to be interpreted is that "half a score and a half" is 10.5 rather than 15. That way the numbers work out better. It is rather ambiguous the way it's written, though, neh?
Posted by Mr.Funny (Member # 4467) on :
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