<p>^^--^^</p>
<p>Different methods are good; some are just better than others. :)</p>
<p>Everybody -
who took part (or intends to do so) in beating a dead horse, Diana, Esther, Lado, and all other nomads which traveled back and forth on foot, by car, bicycle, bus, etc.!
Oh, East is East, and West is West, and never the twain shall meet.
May I suggest declaring a MORATORIUM on skinning and/or executing your tired, your poor rovers by means of patient functions, advanced equations, simple ratios, reasoning actions, sure-fire formulas, Occam razors and all other instruments of penetrating minds.
I wish this moratorium (along with the list of all relevant threads) could become an IMPORTANT stickie, but chances are quite remote. After all, it's just one out of many typical SAT questions.</p>
<p>Nevertheless, here's the list.
<a href="http://talk.collegeconfidential.com/sat-act-tests-test-preparation/28224-qs-full-length-sat-collegeboard-com.html%5B/url%5D">http://talk.collegeconfidential.com/sat-act-tests-test-preparation/28224-qs-full-length-sat-collegeboard-com.html</a>
<a href="http://talk.collegeconfidential.com/sat-preparation/68210-xiggi-s-sat-prep-advice-5.html#post1036240%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/68210-xiggi-s-sat-prep-advice-5.html#post1036240</a>
<a href="http://talk.collegeconfidential.com/sat-act-tests-test-preparation/75306-math-help.html%5B/url%5D">http://talk.collegeconfidential.com/sat-act-tests-test-preparation/75306-math-help.html</a>
<a href="http://talk.collegeconfidential.com/sat-act-tests-test-preparation/36812-sat-math-question-help.html?highlight=distance%5B/url%5D">http://talk.collegeconfidential.com/sat-act-tests-test-preparation/36812-sat-math-question-help.html?highlight=distance</a>
<a href="http://talk.collegeconfidential.com/sat-preparation/452281-question-distance-problems.html%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/452281-question-distance-problems.html</a>
<a href="http://talk.collegeconfidential.com/sat-preparation/453837-why-doesnt-xiggis-formula-work-here.html%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/453837-why-doesnt-xiggis-formula-work-here.html</a></p>
<p>Hey, Trinity, What'd You Say?</p>
<p>My, my.. it looks like the dictum has come down that this conversation is OVER.. :rolleyes:</p>
<p>wow. Large, bold, and red. So tres C4 (college confidential counter-culture).</p>
<p>OK-
The bicycle covers a mile in 12 minutes. The bus covers a mile in 3 minutes. Consecutively, they cover the same distance in 60 minutes.</p>
<p>60= 12X + 3X</p>
<p>X= 4 miles.</p>
<p>Is that better?</p>
<p>
[quote]
So tres C4 (college confidential counter-culture).
[/quote]
</p>
<p>Tr**</p>
<p>I just enjoy math and thought it was interesting seeing the different approaches, a posteriori or not. </p>
<p>And I thought accents were, like colors and font sizes, verboten but now I know better - apparently about all three! :D</p>
<p>Duke, are accents, font sizes and colors verboten? Many students like to report the results of admissions and use fonts and colors. I'll link one for you if you wish! Heck, here is a thread that celebrates the people who were good enough to earn an admission ticket for Yale: <a href="http://talk.collegeconfidential.com/yale-2012/429458-official-early-action-decision-thread.html%5B/url%5D">http://talk.collegeconfidential.com/yale-2012/429458-official-early-action-decision-thread.html</a> </p>
<p>Or could be a misrepresentation by people who truly should know better, but decide to keep fueling horror stories where none ever existed? Isn't the answer to excesses found in .. moderation, especially self-moderation? </p>
<p>Setting aside (forever) the verbal joust that only a few might be able follow, or even enjoy, I am thrilled to read about your interest in math within the context of this forum. While it is far from being a surprise that you'd have a well-developed affinity for different mathematical methods, I'm certain that the many test takers would love to discover more methods that work, especially if they work without fail or flaws. This is what some of us have tried to do, and for a number of years. So, the more the merrier. </p>
<p>As GCF stated --colorfully and forcefully-- finding ways to help students navigate the SAT and learn to avoid its traps is more than one formula and a couple of tricks. And, again, I for one look forward to your continuous contributions in seeking better and faster methods. </p>
<p>Inasmuch as GCF declared it a dead horse, I'd be curious about other methods that could solve the same problem with the following *small *modifications: </p>
<ol>
<li>The speed of the bicycle is not 5 mph, but say 5.6 or 5.175 mph </li>
<li>The speed of the bus is not 20 mph but 27.5 ot 27.175 mph</li>
</ol>
<p>After all, altenative solutions should solve the same problem as quickly and elegantly as before, if only the numbers are altered a bit. It should not change much on the ... reasoning. </p>
<p>So, for the benefit of the students who frequent this board, let's hear it from the "no math needed" gallery. </p>
<p>PS Fwiw, one of the earlier problems about average rate that appeared in the Red Book presented numbers of 5 and 7. So, it's NOT a given that the numbers have to have easy multiples.</p>
<p>I believe the "no math needed" gallery to which xiggi refers prefaced comments with:
[quote]
You don't even need to use math to do this problem.
[/quote]
which is true based on the numbers of this problem. Also, that post exemplifies one of the first rules of standardized tests - "First, do know wrong" - and eliminates 60% of the answers immediately.</p>
<p>As I mentioned before,
it seems to illuminate the difference between "preparing for the SAT" and "preparing to receive an education"
because the use of simple integers in the problem itself leads to a "path of least resistance" that does not necessarily work well with all sets of problems one might reasonably face.</p>
<p>It's a case where using the parallel paths formula works extremely well, so long as the user (a) understands what the answer yielded means and (b) uses the correct mathematical operators in performing it. Alas, in this case, OP missed a bit on both </p>
<p>To respond to one part of xiggi's post above - I actually do not have a goal of helping anyone "navigate the SAT (or) learn to avoid its traps" and will therefore be a dry well when it comes to making "continuous contributions in seeking better and faster methods."</p>
<p>Rather, I am hoping that any effort anyone puts in to studying for and excelling at the SAT, ACT, or whatever else, stems from a real desire to learn qualitative and quantitative reasoning skills and gain experience interpreting and solving a variety of problems that may be more or less buried in real-world situations.</p>
<p>OK, assuming the bike goes 5.6 mph and the bus goes 27.5 mph, </p>
<p>the bike takes 10.7 minutes to go a mile and the bus, 2.2 minutes, so between the two, they went 4.65 miles each way.</p>
<p>Did I get it right?</p>
<p>
[quote]
Did I get it right?
[/quote]
</p>
<p>DP, absolutely. You got the correct answer to the problem.</p>
<p>Now, with your indulgence allow me to show something. It's a bit lengthy but will illustrate something important.</p>
<p>Here's what you did:</p>
<p>
[quote]
OK, assuming the bike goes 5.6 mph and the bus goes 27.5 mph, the bike takes 10.7 minutes to go a mile and the bus, 2.2 minutes, so between the two, they went 4.65 miles each way.
[/quote]
</p>
<p>To follow your convention (expressed in minutes), this would be written out as<br>
Step 1: 60/5.6 = 10.7 and 60/27.5 = 2.2
Step 2: Add them up to get 10.7 + 2.2 = 12.9
Step 3: 60/12.89 = 4.65 </p>
<p>Let's write the same operations as one equation:</p>
<p>60 / [(60/5.6) + (60/27.5)]</p>
<p>And show all the steps to solve
60 / [(60<em>27.5/5.6</em>27.5) + (60<em>5.6/27.5</em>5.6)] or
60 (27.5<em>5.6) / [(60</em>27.5) + (60<em>5.6)] or
60 (27.5</em>5.6) / [60(27.5+5.6)] or
(27.5*5.6) / (27.5+5.6)
Solve = 4.65 </p>
<p>What was that all about? What was the final equation?
(27.5 * 5.6) / (27.5 + 5.6) </p>
<p>Isn't that also S1 * S2 / S1 + S2? Doesn't that look familiar? </p>
<p>The long and the short of the story is that the steps you followed were both correct and a correct application of the d =r*t basic formula. All what the quick formula accomplishes is providing a quick and safe ... shortcut. </p>
<p>Please note that explanation would have been a lot easier by using 1 instead of 60 (1 hour instead of 60 minutes.) I used 60 minutes as base to follow the numbers you used in your answer. Also note that the "explanation" is obviously NOT required to solve the problem. It simply shows how your approach is ... one and the same as the quicker formula. </p>
<hr>
<p>PS Same thing expressed in hours (easier to follow)
Step 1: 1/5.6 = 0.1786 and 1/27.5 = 0.03636
Step 2: Add them up to get 0.2149
Step 3: 1 / 0.2149 = 4.65 </p>
<p>Let's write the operations as one equation:</p>
<p>1 / [(1/5.6) + (1/27.5)]</p>
<p>And show all the steps to solve
1 / [(1<em>27.5/5.6</em>27.5) + (1<em>5.6/27.5</em>5.6)] or
1 (27.5<em>5.6) / (27.5 + 5.6) or
(27.5</em>5.6) / (27.5 + 5.6)
Solve = 4.65</p>
<p>.... So, if the C4's ran a Halfback option play, and the C5's rode back in on their high horses... oh... never mind....</p>
<p>Yea so maybe after all this yabba yabba yabba..... maybe the tiltle of this thread should be changed to ... Why does Xiggi's method work here too? (it does afterall)</p>