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Two trains travel at constant speeds. What is the ratio of the slower

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New post 26 Mar 2019, 10:58
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C
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  65% (hard)

Question Stats:

39% (01:51) correct 61% (01:07) wrong based on 18 sessions

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GMATH practice exercise (Quant Class 19)

Two trains travel at constant speeds. What is the ratio of the slower speed to the faster speed?

(1) The time it takes for one train to pass the other when they are in the same direction is 3h.
(2) The time it takes for one train to pass the other when they are in opposite directions is 2h.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Two trains travel at constant speeds. What is the ratio of the slower  [#permalink]

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New post 26 Mar 2019, 15:10
fskilnik wrote:
GMATH practice exercise (Quant Class 19)

Two trains travel at constant speeds. What is the ratio of the slower speed to the faster speed?

(1) The time it takes for one train to pass the other when they are in the same direction is 3h.
(2) The time it takes for one train to pass the other when they are in opposite directions is 2h.

\({\rm{faster}}\,\,{\rm{train}}\,\,\left\{ \matrix{
\,x\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr
\,A\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.\)

\({\rm{slower}}\,\,{\rm{train}}\,\,\left\{ \matrix{
\,y\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr
\,B\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.\)

\(? = {B \over A}\,\,\,\,\,\,\,\left[ {A > B > 0} \right]\)


Image


\(\left. \matrix{
\left( 1 \right)\,\,A - B = {{y + x} \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{trivial}}\,\,{\rm{bifurcation}}\,\, \hfill \cr
\left( 2 \right)\,\,A + B = {{y + x} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{trivial}}\,\,{\rm{bifurcation}} \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {1 + 2} \right)} \,\,\,\,3\left( {A - B} \right) = 2\left( {A + B} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,A = 5B\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Two trains travel at constant speeds. What is the ratio of the slower   [#permalink] 26 Mar 2019, 15:10
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