Bunuel wrote:
A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
A. 36
B. 40
C. 42
D. 54
E. 65
Let´s solve this problem without taking into account the "examiner´s generosity" (in terms of inviable alternative choices) nor exploring particular cases.
(Both approaches are important. We just want to avoid repetitions and present the
UNITS CONTROL, one of the most powerful tools of our method!)
\(A \to B\,\,:\,\,\,\,\,\left\{ {\,\frac{{60\,\,{\text{yards}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,;\,\,\,\,\,2x\,\,{\text{yards}}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to C\,\,:\,\,\,\,\left\{ {\,\frac{{45\,\,{\text{yards}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,;\,\,\,\,\,\,x\,\,{\text{yards}}} \right.\)
\(? = \frac{{{\text{# }}\,\,{\text{total}}\,\,{\text{yards}}}}{{{\text{# }}\,\,{\text{total}}\,\,{\text{seconds}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{{2x + x}}{{\frac{{2x \cdot \boxed3}}{{60 \cdot \boxed3}} + \frac{{x \cdot \boxed4}}{{45 \cdot \boxed4}}}}\,\, = \,\,\frac{{3 \cdot x \cdot 18 \cdot 10}}{{10 \cdot x}} = 54\,\,\,\,\left[ {\frac{{{\text{yards}}}}{{{\text{second}}}}} \right]\)
\(\left( * \right)\,\,\,\,\,\frac{{\left[ {\,{\text{yard}}\,} \right]}}{{\,\,\,\left[ {\,\frac{{{\text{yard}}}}{{{\text{second}}}}\,} \right]\,\,\,}} = \,\,\left[ {\,{\text{second}}\,} \right]\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here:
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