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<p>I am not sure what you mean about having to understand the derivations. I wrote that one has to understand how and when to use a formula. While it is interesting to know the basis of the formula, this is not required to apply it. Just at it is not necessary to know how the Pythagoras’ theorem was created to apply it on the SAT.</p>
<p>@Xiggi, that is a very good point you made about how the slight chance could make the problem difficult to solve without a formula. I suppose in that case, the formula is definitely a much better option.</p>
<p>hi there, xiggi: </p>
<p>regarding this: Bernardo drives to work at an average speed of 37 miles per hour and returns along the same route at an average speed of 23 miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?</p>
<p>um well in my post i delineated 2 methods to do this. the quick easy way was ratio which worked very well in that problem, and it would still work here. but i honestly wouldnt want to mess with a really ugly ratio, so i’d go with the system of equations which wouldnt take more than 1-2 minutes at most. also y am i asked to not used a calculator, i dont see any point now or in the future where i would have to do that. </p>
<p>I think you make it clear though when you say you have to understand HOW to use the formula, and if you dont like me, well then you will get it wrong. so after I had a bad experience, I just decided to stick with things that were intuitive to me. Not sure how things work for others, but it tends to be a fool proof method for me.</p>
<p>So nyway what I’m saying is, the opportunity cost of having to try a risky manuever (for ME atleast) just doesn’t out weight the for sure intuitive method that I have. I understand your point about the speed, but accuracy comes first. I just can’t derive the formula and don’t know how it works, so I shouldnt be using it just the same other like me shouldnt be using it either.</p>