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

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

by [email protected] » Tue Mar 26, 2019 9:45 am

00:00

A

B

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D

E

## Global Stats

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

by [email protected] » Tue Mar 26, 2019 1:57 pm

00:00

A

B

C

D

E

## Global Stats

[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.
$${\rm{faster}}\,\,{\rm{train}}\,\,\left\{ \matrix{ \,x\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr \,A\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.$$
$${\rm{slower}}\,\,{\rm{train}}\,\,\left\{ \matrix{ \,y\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr \,B\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.$$
$$? = {B \over A}\,\,\,\,\,\,\,\left[ {A > B > 0} \right]$$

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