I was reading Xiggi's thread and he had this great formula to a math problem.........

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<p>and I have a question about it.</p>

<p>A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took 1 hour, how many miles is the round trip.</p>

<p>Okay I understand he uses the formula (2xspeed1xspeed2)/(speed1+speed2).</p>

<p>But let's say the round trip took 3 hours long. What must be changed to do the problem. I know how to do the problem the long way when using this criteria, but not the short way, xiggi's method.</p>

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<p>You cant use the formula when it asks for 3 hours. You're better off doing it the long way then trying to manipulate that equation to suit 3 hours.</p>

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<p>you can actually. Just multiple the answer by 3.</p>

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<p>WHAT
10char.</p>

5

<p>yeah
(2xspeed1xspeed2)/(speed1+speed2). is an incomplete formula. I've noticed that the real formula ought to be (2 x Time x speed 1 x speed 2)/(speed 1 + speed 2).... the Time is usually skipped since it's mostly 1. But if it is 3, plug it in.</p>

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<p>The "long" way isn't even that long...It takes probably 20seconds more?
I honestly prefer the "long" way to that formula as it is more reliable. The formula to me just seems like blind faith,,</p>

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<p>I agree with shiomi: </p>

<p>8 mi / hr * x hr = 12 mi / hr * y hr (because the distance is the same both ways) </p>

<p>x+y = 1 (one hour total; or change this to three)</p>

<p>Basically you have a system of two equations, really easy to solve. That didn't take long at all. And now we all feel more confident. </p>

<p>8x=12y
x+y=1
x+8x/12=1
x+2x/3=1
5x/3=1
x=3/5 hr
y=2/5 hr </p>

<p>4.8 miles </p>

<p>OR </p>

<p>8x=12y
x+y=3
x+8x/12=3
x+2x/3=3
5x/3=3
x=9/5 hr
y=6/5 hr </p>

<p>14.4 miles </p>

<p>So yes you can just multiply it by 3, but the reason why I advocate shiomi's view is:
Notice that I got the right answer right away. Math isn't about blind faith. That's what makes it so beautiful. There was no uncertainty, no guesswork. I knew I was right because I proved that I was right using basic logical intuition. I don't rely on formulas to tell me what's right. The way to go is to derive your equations. Even the very basic ones, like the areas, volumes, etc. (when you learn calc). It really helps because you actually know what you're doing.</p>

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<p>
[quote]
Notice that I got the right answer right away. Math isn't about blind faith. That's what makes it so beautiful. There was no uncertainty, no guesswork. I knew I was right because I proved that I was right using basic logical intuition. I don't rely on formulas to tell me what's right. The way to go is to derive your equations. Even the very basic ones, like the areas, volumes, etc. (when you learn calc). It really helps because you actually know what you're doing.

[/quote]
</p>

<p>Interesting!</p>

<p>Since is when knowing what to do equivalent to ... blind faith? Since when is knowing how to "derive" and apply the correct formula after understanding a problem correctly equal to uncertainty or guesswork? </p>

<p>Fwiw, it might be helpful for someone who believes in deriving his own equations to do some work on the "long formula" and "long way" and understand the origin of shorter formula, and understands WHY certain numbers are multiplied by 2. This might help AVOID the silly mistake presented in the "better solution." </p>

<p>Doing well on the SAT has absolutely nothing to do with "proving" to be right. It has everything to do with finding the correct answer in the easiest and most elegant way. </p>

<p>Student who decide to work a problem the long way are simply falling in the College Board trap. </p>

<p>PS It is also important to understand a formula and its expression. The basic rules of d,r, and t are still to be respected.</p>

<p>PPS Using the correct formulas also tends to yield the CORRECT answer. :D</p>

<hr>

<p>For the problem: A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took THREE hours, how many miles is the round trip.</p>

<p>**Is this the correct answer? ** Since when is traveling 3 hours at the harmomic average speed of 8 and 12 mph yielding a distance of 14.4 m? </p>

<p>
[quote]
</p>

<p>Basically you have a system of two equations, really easy to solve. That didn't take long at all. And now we all feel more confident. </p>

<p>8x=12y
x+y=1
x+8x/12=1
x+2x/3=1
5x/3=1
x=3/5 hr
y=2/5 hr </p>

<p>4.8 miles </p>

<p>OR </p>

<p>8x=12y
x+y=3
x+8x/12=3
x+2x/3=3
5x/3=3
x=9/5 hr
y=6/5 hr </p>

<p>14.4 miles </p>

<p>So yes you can just multiply it by 3, but the reason why I advocate shiomi's view is:

[/quote]
</p>

<p>Indeed, it really helps when you know what you're doing ... when you actually DO!</p>

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<p>I have another method to share. It's just as fast as Xiggy's, and doesn't require any formulas at all.</p>

<p>I give you: Plugging in </p>

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<p>
[quote]
I give you: Plugging in </p>

11

<p>
[quote]
Since when is traveling 3 hours at the harmomic average speed of 8 and 12 mph yielding a distance of 14.4 m?

[/quote]
</p>

<p>I didn't give the round trip distance (just one way). I guess that just goes to show that it's important to answer the question that is being asked, which is something I am sure we both can agree on. I hope you don't intend to be condescending :) Actually, to be fair, I probably didn't finish solving the problem here. The truth is, I could have made the same mistake (if it was one) regardless of the method used, so that can't be used to discredit my argument. </p>

<p>
[quote]
Student who decide to work a problem the long way are simply falling in the College Board trap.

[/quote]
</p>

<p>I beg to differ. Students who decide to work a problem with the sole intent of doing whatever it takes just to come up with an answer are playing into the trap. The trap, the notion that bad standardized test scores mean the end of the world and the intense competition and stress that is perpetuated by this. The student cannot let a number define himself/herself. In contrast, a student who may take a little longer in the short run benefits in the long run by an intellectual exercise.
Anybody can memorize a formula. Kid X can memorize the volume of a sphere, 4/3<em>pi</em>r^3, for example. Kid Y can also do nothing but memorize. Here's a little experiment: Tell Kid Y that the formula instead is 4/5<em>pi</em>r^3. Guess what? Kid Y will think that's correct, simply because s/he is told that it is. Nothing further than that. It kills intellectualism. It kills the pursuit of knowledge, our sustenance and vitality.
Another example: Kid X memorized the volume formula for a sphere. Kid Y derived it. Now a question asks for the volume of a cone. Kid X doesn't know because s/he's stuck in a little box. Kid Y knows the technique by which one can derive an expression that gives the volume of any arbitrary figure. Who wins in the long run? </p>

<p>Take the OP for example. No offense intended, but this thread wouldn't exist had the OP not treated the equation as a formula to be memorized.

[quote]
I know how to do the problem the long way when using this criteria, but not the short way, xiggi's method.

[/quote]

The OP could have derived your method if s/he could do it the long way. No confusion could exist then. </p>

<p>Xiggi, although I disagree with your view, I respect you and the vast assistance that you have provided the CC community.

[quote]

Doing well on the SAT has absolutely nothing to do with "proving" to be right. It has everything to do with finding the correct answer in the easiest and most elegant way.

[/quote]

It's just that math (real math) is all about rigorous proofs; and the austerity and beauty of mathematics is being neglected, to which I am adamantly opposed.</p>

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<p>Okay thanks for the help everyone, but honestly I do not care at all about the principles and origins of math formulas during the SAT. So I will heed to using this formula:</p>

<p>(2 x Time x speed 1 x speed 2)/(speed 1 + speed 2)</p>

<p>topic is over, stop arguing.</p>

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<p>I have to say, that is truly sad: I don't care about math, I just want an 800 on Math.</p>

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<p>Lol, what a poor mindset to go about taking the SATs. You should always care.</p>

<p>Im sad.</p>

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<p>It's all about preference, so whatever method you like more, use it.</p>

<p>I prefer the "long" way of doing it, because it gives me more confidence.</p>

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<p>what the hell? whats the answer? i got 9.6</p>