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

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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.

Answer: [spoiler]______(C)__[/spoiler]
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[email protected] 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).


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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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