NOTE: this problem is missing ALL the parentheses in denominators. this makes the answer choices misleading.
every one of the answer choices is supposed to be a single fraction.
for instance, (a) and (b) are fractions with denominator (x + y), etc.
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the above poster's solution is good.
here are some other things about this problem:
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* you can PLUG IN NUMBERS.
this is not entirely easy to do; you have to select an x, y, z that don't make the numbers too ugly. however, it can certainly be done.
if you want to see a specific example of plug-in-numbers for this problem, go ahead and post back.
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* you can use PROCESS OF ELIMINATION. here are easy ways to eliminate three of the choices:
since the "regular" train is slower than the high-speed train, y must be greater than x.
since y is greater than x, (b) and (d) are negative numbers, and are thus wrong.
if x = y, then the answer to the problem must be zero (because the two trains would then be moving at the same speed, despite the designation of one of them as "fast" and the other as "slow").
choice (c) is not zero if x = y (in fact it's infinity!), so it's wrong.
that leaves (a) vs. (e).
you can choose between these two if you take a slightly more complicated tack: use UNITS.
the units of choice (a) are (miles * hours) / hours, which works out to miles. this is as required.
the units of choice (e) are (hours * hours * hours) / hours, which works out to hours squared. that makes no sense.
you can also eliminate choice (d) on this basis, too.
we're left with (a).
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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