Why doesnt Xiggis Formula work here?

Test Preparation SAT Preparation
1

<p>Lado rode her bicycle to the repair shop and rode the bus home by the same route. Excluding the time she spent at the shop, she spent a total of 1 hour traveling from her home to the shop and back again. If she rode her bicycle at an average speed of 5 miles per hour, and the bus traveled at an average speed of 20 miles per hour then for how many miles did she rider bicycle?</p>

<p>A) 2
B) 4
C) 5
D) 8
E) 10</p>

<p>Okay so i see this problem and i am like woot an "xiggi problem" so i quickly go</p>

<p>2 * rate1 * rate 2 / rate 1 + rate 2</p>

<p>and then i get some how 2 ? by just doing 2 * 5 * 20 / 5*20</p>

<p>the answer though happens to be B 4?</p>

<p>Can anyone explain why the method failed or what i did wrong in this case??</p>

2

<p>You add the rates for the denominator, you don't multiply them. You get 8, which is the average speed for traveling one hour, which is 8 miles. Divide that by two to get 4 miles, the answer.</p>

3

<p>Xiggi this, Xiggi that. Where would we all be without Xiggi to provide us our common sense. It is enough to make my stomach rise. Anyway, here is a method of solving that is a little less abstruse than using Xiggi's formula.</p>

<p>d = rt (take this to heart)</p>

<p>d = 5x miles
d = 20y miles
x + y = 1 hr</p>

<p>Substituting for x and setting the two equations equal to each other:
5(1 - y) = 20y
y = 1/5
d = 4 miles</p>

4

<p>I would do alpha's method if I were checking my work; if I were zooming through these problems, I would use the quick 2ab/a+b formula and be done with it. That type of error that you made, 5*20 instead of 5+20, can be your downfall. It can cause more problems wrong than questions that you had no clue how to do. You have to teach yourself to go both slowly and quickly, as in knowing exactly what you're doing and how each step relates to the problem while doing it quickly.</p>

5

<p>Abstruse? </p>

<p>As in hard to understand, recondite, esoteric or as in obsolete, secret, or is it hidden. </p>

<p>Okay!</p>

6

<p>Its been so long since I did this stuff-- but I just looked at the possible answers.. Obviously if Lado travelled for an hour total, and both rode a bike and the bus, and rode at a rate of 5 mph on the bike, then only choices A and B are possible. A quick playing with the ratios produces 4/5 for the bike and 4/20 (1/5) for the bus. Very reductionistic, but it works!</p>

7

<p>
[quote]
Abstruse?

[/quote]

I am partial to this definition: "beyond ordinary knowledge or understanding." The formula may be easy enough to memorize, but the student will need not second guess himself, out of fear or uncertainty, if he follows the easily followable method I outlined. It takes not much longer and error that would be fatal might be avoided, such as in this case.</p>

8

<p>Two things.</p>

<p>A) I am getting 8 as an answer. 2(100/25)
B) This may have been asked already, but if the SAT asks one of these types of problems, is it always going to be the distance in 1 hour?</p>

9

<ol>
<li><p>The question asks for the just one of the distances, not total distance. Divide 8 by 2 to get 4, the same distance throughout. </p></li>
<li><p>Most of the time it is 1 hour, but anything can always pop up. I would still expect 1 hour most of the time though.</p></li>
</ol>

10

<p>after I read the prompt it took me 30 seconds to do it, and I did it mentally without any formula.</p>

<p>The time is one hour, the bus goes 20mph the bicycle goes 5mph. That means the bus goes 4 times faster the bike. You have sixty minutes, so that means that the time it took by bus, plus 4 times that gives you 60. I tried with 10 first. 10 + 10.4 = 50. So it was a bigger number, and it wasn't hard to tell that the answer was twelve. 12 + 12.4 = 60 So twelve is 1/5 of 60 (These things if you have the natural skill of math/heavy practice you know them by heart) So 20 miles per hour multiplied by 1/5 is 4 miles.</p>

11

<p>
[quote]
Abstruse? I am partial to this definition: "beyond ordinary knowledge or understanding." The formula may be easy enough to memorize, but the student will need not second guess himself, out of fear or uncertainty, if he follows the easily followable method I outlined. It takes not much longer and error that would be fatal might be avoided, such as in this case.

[/quote]
</p>

<p>The "fatal" error had nothing to do with an incorrect application of a formula. The error was nothing more than a mere inattention to an important detail. Unfortunately, a small inattention in reading the question correctly is the difference between right and .. wrong. The OP did not see that the question asked was ... the distance on a bicycle only. Regardless of the method used or the number of steps needed to solve a problem, there is NO recovery for reading a question incorrectly. </p>

<p>
[quote]
Xiggi this, Xiggi that. Where would we all be without Xiggi to provide us our common sense. It is enough to make my stomach rise. Anyway, here is a method of solving that is a little less abstruse than using Xiggi's formula.</p>

<p>d = rt (take this to heart)</p>

<p>d = 5x miles
d = 20y miles
x + y = 1 hr</p>

<p>Substituting for x and setting the two equations equal to each other:
5(1 - y) = 20y
y = 1/5
d = 4 miles

[/quote]
</p>

<p>Of course, that will work ... and require about fifteen steps to write down the formula, set up the equations correctly, and hoping that no mistake is made in substituting terms. </p>

<p>In the meantime, I think I'll stick to the abstruse and cling to my stomach churning but ever so limpid and safe formula. A formula I'm assuming you know is entirely derived from the d = rt you suggest "to take to heart." </p>

<p>In this case, my work paper would show only </p>

<p>Line 1: bicycle ... 1/2 distance (1/2)
Line 2 : s1<em>s2 / s1 + s2
Line 3= 5</em>20 / 5+20
Line 4= 100/25 = 4 </p>

<p>I estimate that at the time I'd be bubbling B, you'd be at step 3 or maybe step 4 in your fifteen step solution. </p>

<p>Of course, I could also have pointed out why TCB does not seem to offer an answer different from B for its harmonic average problems, or why TCB knows it can always count on less than astute students applying a correct but overly time wasting method. After all, they know the value of ... time in Princeton!</p>

12

<p>Here's another way to do it:</p>

<p>5 miles/hour --> 12 mins/mile
20 miles/hour-->3 mins/mile</p>

<p>Every mile biked will need to be paired with a mile by bus (covering the same distance both ways)</p>

<p>Since 1 mile by bike + 1 mile by bus uses up 15 minutes, you can see that the person in the problem could have only biked 4 miles in the time allowed by the problem.</p>

13

<p>For the SAT, I like Xiggi's way the best :D</p>

14

<p>Cocalait... i wish i had that flexible mind of yours... I am under this fear that anyother way other than the 'formula' way for math would yield an answer that i'll have to recheck. I mean does a couple of seconds count..? Today I realise (just did SAT) that it does!! coz u have a couple of qs. at the end which are entirely new. Anyway:</p>

<p>x/5 + x/20 = 1
After this ... proceed mentally as follows:
x(1/5+1/20)=1
x{ (4+1)/20 } = 1
x= 20/5=4 ...........................all these steps are NOT necessary...just put it here for understanding.</p>

<p>x is the unknown miles. Ofcourse since its mi/h ... inorder to get hours on top u make it (h/mi) and the multiply by (mi) to get the hours. Simple? well it revolves around this idea---> mi/h that's all.</p>

15

<p>advancer07, you could've done htis:</p>

<p>x/5 + x/20 = 1
x/5(1 + 1/4)=1
x/5(5/4)=1
x/4=1
x=4</p>

16

<p>u caught me...(i m no good at factorisation) Actually no difference... however i like to keep x separate.</p>

17

<p>I've used all the other formulae outlined here during some point of my high school, and I must say I like the one outlined by Xiggi the best. It's quite simple if you have a grasp of what the question wants.</p>

18

<p>
[quote]
that will work ... and require about fifteen steps

[/quote]

“Fifteen steps” is quite an exaggeration. It makes me wonder why you would wish to so dissuade someone from using the method I proposed. And, it appears to me that the OP is not at fault for a misreading of the question, but for a misunderstanding of the equation (specifically, of what the equation produces), which on its face is not immediately understandable, though indeed it is derived from the elementary equation d=rt. Perhaps the OP would not appreciate your unkind doubt of his reading abilities.</p>

<p>It is noteworthy to note that your shortcut works only when the total time is 1 hour. If TCB is as villainous as you describe, what better way to prove this than to part with tradition and trip up a large proportion of students (and an even greater proportion of Xiggi disciples) by including a problem having a total time of something other than an hour? Anyway, what is so special about an hour, that TCB would be so disinclined to part with it? How tragic it would be if a student becomes dazed and confused by such a simple variation, and utterly hopeless for he knows naught but 2s1*s2 / s1 + s2.</p>

<p>To each his own preference, but I would like to reassert that d=rt, in all its glory, provides a fool-proof, easily-understandable method of solving the type of problem put forth by the OP.</p>

19

<p>
[quote]
“Fifteen steps” is quite an exaggeration. It makes me wonder why you would wish to so dissuade someone from using the method I proposed. And, it appears to me that the OP is not at fault for a misreading of the question, but for a misunderstanding of the equation (specifically, of what the equation produces), which on its face is not immediately understandable, though indeed it is derived from the elementary equation d=rt. Perhaps the OP would not appreciate your unkind doubt of his reading abilities.

[/quote]
</p>

<p>Alpha, my reasons to dissuade somone from using the basic d = rt are pretty smple: it's lengthy, error-prone, and there is something much better and much more elegant. </p>

<p>How do I know that? By reading the boards for the past 4 years and seeing the same questions coming up again and again. This distance problem seemed to trip a large number of students who, despite understanding the basic formula, could not set the equations up correctly, and ended up falling in the two trap of TCB: picking the arithmetic average or having to pick between B and D (as PR recommends.) In all cases, the student also wasted time on the problem. </p>

<p>As far as TCB/ETS' uses of ONE HOUR, a little knowledge of standardized tests might help you understanding the reasons behind keeping the answer within the grasp of students and within a reasonable limit. So far, TCB, on the SAT Reasoning Test, has used as sole variance the one way or two distance ... and this has been enough to keep the question as one of the final and most difficult question. Once this type of question stops yielding the expected "range" results, it would be easy to add bells and whistles such as changing the total time or adding legs to the trip. However, a quick and safe-proof answer will remain available via a variance of the formula presented here. Harmonic mean will not disappear from the math books! And neither will the abiliy of students to reduce fractions. </p>

<p>Regarding "Perhaps the OP would not appreciate your unkind doubt of his reading abilities." I described a "mere inattention" to an important detail ... the detail that directly caused the wrong error. Misreading the question was the culprit, and as fas as I know, that symptom is omnipresent in many of the errors reported at College Confidential. And, this is not a great surprise for a test that requires reasoning and concentration under timed limits. </p>

<p>And, Last, but not least, may I suggest you taking some time to review your own manner of delivering "kind" comments and think about your own tendencies to make gratuitous attacks. </p>

<p>To each his own preference is indeed true. There are many ways that lead to the top of the mountain! Some methods are better than others, and it requires a bit of specific knowledge and experience to appreciate the differences. In the meantime, it's quite easy to let the members of this forum decide what works for them. </p>

<p>Best of luck with your stomach!</p>

20

<p>In my business, there is a test that we give patients that looks at "executive function" (problem solving) skills. In some cases people think the test is far more complicated than it is, and use a complex strategy when a simple one is in order. I mention this because in this case, one only has to THINK about the problem, and doesn't really need to plug in any formulas. It only takes a second. Follow me here:</p>

<p>1) As I mentioned above, if the rider rides both her bike and the bus equal distances, and spends a total of an hour in transit, then logically answers C,D and E are immediately eliminated, because if she rides her bike at a rate of 5mph then "C" isn't possible because she'd only have ridden her bike, not the bike and the bus if she travelled 5 miles; and "D and E" aren't possible because she couldnt have ridden MORE than 5 miles one way in an hour total. So instantaneously it is easy to eliminate the last 3 choices and see that only A or B are possible. </p>

<p>2) Then, it is easy to realize that "A" isnt possible because if she only travelled 1 mile each way, it wouldnt take her an hour, because she can ride 5 miles in an hour (1 mile in 12 minutes) and the bus goes faster than the bike. So travelling 2 miles total is going to take a total of 15 minutes (and you don't even need to do these calculations-- its just obvious that she can make it there and back in less than an hour if she's only going a total of 2 miles).</p>

<p>So , if you just THINK about the problem for a second and look at the answers, it very quickly (well, at least to me) becomes obvious that the only possible answer is B. To double ck, I plugged in the mileage (48 min. on bike, 12 min. on the bus). No potential for making a silly math error when you just think about it logically of a second. Now, that said, I am sure there are plenty of people who think that using a canned formula is "faster". IMO, this was really quick to just reason out, without no stinkin' formula :)</p>