<p>I heard there is a simple formula to do the Average Rate questions. Could someone tell me (and explain) what it is please? If you found any other methods that makes average rates questions easier please comment. </p>
<p>I am trying to boost my Math score from a 690 to at least a 750.</p>
<p>Start by reading these threads…should do it.</p>
<p>site:talk.collegeconfidential.com xiggi’s formula</p>
<p>(Search google for “Xiggi’s Formula” - then select more results from College Confidential)</p>
<p>Thanks…=)</p>
<p>Basically, if you’re traveling a distance of x1 at a rate of r1, then a distance of x2 at a rate of r2, your average speed is just the total distance over total time, or</p>
<p>(x1 + x2)/((x1/r1) + (x2/r2))</p>
<p>If x1 = x2 (e.g. you’re traveling back and forth) then your average speed is equal to</p>
<p>2x1/((x1/r1) + (x1/r2)), which simplifies to 2(r1 + r2)/(r1*r2). This is also equal to the harmonic mean of r1 and r2.</p>
<p>I don’t know how useful this “formula” is, since it only works when the two distances are equal. Plus it’s really easy to do by hand.</p>
<p>The formula is 2(a*b)/(a+b).</p>
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<p>Well, it so happens that most roundtrips have the same distance both ways. At least, in the ETS world. :)</p>
<p>Simply stated, it will never hurt anyone to know how to apply the harmonic mean formula, and it will make a tester really happy to recognize a problem of average speeds. </p>
<p>And speaking of simplicity, the solution is indeed quite simple, but the question (when it appears) remains a high level question and remains a potential timesink for anyone who clings to the simplistic distance/rate/time formula of middle school.</p>
<p>Yeah, I guess it could be useful…oh well, never really used the harmonic mean in high school math other than AM-GM-HM inequality. Got an 800 and 36 on SAT/ACT math anyway.</p>
<p>I think I read something on your thread Xiggi that said that the answer is always “b” for these problems and so far that has been right for about 8 problems. </p>
<p>Thanks guys. The formula is perfect.</p>
<p>The way ETS presents the problem in a MC setting leads to the answer being B. However, it is important to understand why this and even more important to read the question and choices carefully. If the two speeds are 6 and 12, the choices should be:</p>
<p>A. 6
B. Something between 6 and 9
C. 9 (straight average)
D. Something between 9 and 12
E. 12</p>
<p>C is the trap answer and A and E are obviously wrong. But, again, READ the choices to see ETS does not flip it around.</p>
<p>Well that’s because the harmonic mean of two positive numbers a and b (with a < b) is always between a and (a+b)/2, because</p>
<p>(a+b)/2 > sqrt(ab) > 2/(1/a + 1/b) by the AM-GM-HM inequality,</p>
<p>and 2/(1/a + 1/b) > a → 2 > a(1/a + 1/b) = 1 + a/b, which is true (because we assumed a < b).</p>
<p>So the answer to these type of questions is always between the smallest # and the arithmetic mean of the two #s.</p>
<p>Yep, yep … and it seems like yesterday that I started repeating the same thing. </p>
<p><a href=“http://talk.collegeconfidential.com/329850-post6.html[/url]”>http://talk.collegeconfidential.com/329850-post6.html</a></p>
<p>Many yesterdays! :)</p>
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<p>Forgot to say “Congrats” and thank you (on behalf of the next generations) for spending your time helping others understand the tests better. </p>
<p>X</p>
<p>@xiggi thanks 
Yeah, no problem…</p>