NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 14:17 It is currently 27 Apr 2024, 14:17
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Two trains cross each other in time T, when they are

User avatar
krisrini
Manager
Manager
Joined: 15 Apr 2005
Posts: 159
Own Kudos [?]: 32 [0]
Given Kudos: 0
Location: India, Chennai
Send PM
Two trains cross each other in time T, when they are [#permalink] New post   05 Jan 2006, 04:25
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 3 sessions
Hide Show timer Statistics
Two trains cross each other in time T, when they are travelling in opposite directions. The faster train completely overtakes the slower train in time t if they are travelling in the same direction. If the trains are equal length, how long will the faster train take to completely overtake the second train, when the first one is in rest?

a) Tt/2(T+t)
b) (T-t)/(T+t)
c) (T+t)
d) 2Tt/(T+t)

Thanks
Sreeni



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
giddi77
Director
Director
Joined: 21 Sep 2003
Posts: 528
Own Kudos [?]: 257 [0]
Given Kudos: 0
Location: USA
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   05 Jan 2006, 05:50
D)

s1 = speed of faster
s2 = speed of slower
L = length of the train

When trains are crossing in opp directions:
It is exactly same as a situation where, the faster train were travelling at at a speed s1+s2 and the slower would be stopped. (Please ignore grammar)

The distance it travels is length of the train (L)
L = (s1+s2)*T ---(1)

When the trains are travelling in the same direction:
It is exactly same as a situation where, the faster train were travelling at at a speed s1-s2 and the slower would be stopped. (Same distance L)
L = (s1-s2)*t --- (2)

(1)&(2) give:

(s1+s2)*T = (s1-s2)*t

or s1/s2 = (T+t)/(t-T) --(3)

Finally, when the slower train is stopped, the faster train has to travel the same distance L.

Time = L/s1
Using L from (1)
= (s1+s2)*T/s1
= (1+s2/s1)*T
Using the inverse of (3) here gives
= 2*t*T/(T+t)


Hope this is correct and these kind of problems dont appear in GMAT :( :?: :twisted:
User avatar
hkm_gmat
Manager
Manager
Joined: 05 Jan 2005
Posts: 132
Own Kudos [?]: 24 [0]
Given Kudos: 0
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   05 Jan 2006, 18:45
Good Question , keep them coming. Let us know the source.

Ans D

Let
L be the length of the Train
S be the speed of the slow Train
F be the speed of the fast Train


We have :

1. 2L/(F+S) = T

2. 2L/(F-S) = t

solving 1 & 2

F = L(t+T)/tT

we need to find 2L/F

= 2tT/T+t
User avatar
allabout
Manager
Manager
Joined: 17 Dec 2005
Posts: 232
Own Kudos [?]: 74 [0]
Given Kudos: 0
Location: Germany
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 04:45
hkm_gmat wrote:
Good Question , keep them coming. Let us know the source.

Ans D

Let
L be the length of the Train
S be the speed of the slow Train
F be the speed of the fast Train


We have :

1. 2L/(F+S) = T

2. 2L/(F-S) = t

solving 1 & 2

F = L(t+T)/tT

we need to find 2L/F

= 2tT/T+t


It aren't two "lenghts" but one length that is passed by a train with speed s1+s2. In case this is unclear: Imagine two trains cross each other; they actually don't pass two lengths but one in a faster time.

Maybe this hint is useless or idle, but maybe it is helpful for other questions.
However in this case it doesn't matter since you use two lenghts in both statement 1 and 2.
User avatar
SunShine
Manager
Manager
Joined: 11 Nov 2005
Posts: 129
Own Kudos [?]: 54 [0]
Given Kudos: 0
Location: London
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 15:05
I think the two equations are not right. please see the red part...

giddi77 wrote:
D)

s1 = speed of faster
s2 = speed of slower
L = length of the train

When trains are crossing in opp directions:
It is exactly same as a situation where, the faster train were travelling at at a speed s1+s2 and the slower would be stopped. (Please ignore grammar)

The distance it travels is length of the train (L)
L = (s1+s2)*T ---(1) it should be 2L
When the trains are travelling in the same direction:
It is exactly same as a situation where, the faster train were travelling at at a speed s1-s2 and the slower would be stopped. (Same distance L)
L = (s1-s2)*t --- (2)

(1)&(2) give:

(s1+s2)*T = (s1-s2)*t

or s1/s2 = (T+t)/(t-T) --(3)

Finally, when the slower train is stopped, the faster train has to travel the same distance L.

Time = L/s1
Using L from (1)
= (s1+s2)*T/s1
= (1+s2/s1)*T
Using the inverse of (3) here gives
= 2*t*T/(T+t)


Hope this is correct and these kind of problems dont appear in GMAT :( :?: :twisted:
User avatar
SunShine
Manager
Manager
Joined: 11 Nov 2005
Posts: 129
Own Kudos [?]: 54 [0]
Given Kudos: 0
Location: London
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 15:08
The two equations are not right in my opinion. please see the red part...

hkm_gmat wrote:
Good Question , keep them coming. Let us know the source.

Ans D

Let
L be the length of the Train
S be the speed of the slow Train
F be the speed of the fast Train


We have :

1. 2L/(F+S) = T

2. 2L/(F-S) = t it should be L
solving 1 & 2

F = L(t+T)/tT

we need to find 2L/F

= 2tT/T+t
User avatar
SunShine
Manager
Manager
Joined: 11 Nov 2005
Posts: 129
Own Kudos [?]: 54 [0]
Given Kudos: 0
Location: London
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 15:16
From my working, the time it takes to completely overtake the second train, when the first one is in rest =2LTt/(2Lt+LT)


THE ANOTATIONS ARE SAME AS GIDDI77 HKM_GMAT!

by the way what is OA/OE?


krisrini wrote:
Two trains cross each other in time T, when they are travelling in opposite directions. The faster train completely overtakes the slower train in time t if they are travelling in the same direction. If the trains are equal length, how long will the faster train take to completely overtake the second train, when the first one is in rest?

a) Tt/2(T+t)
b) (T-t)/(T+t)
c) (T+t)
d) 2Tt/(T+t)

Thanks
Sreeni
User avatar
giddi77
Director
Director
Joined: 21 Sep 2003
Posts: 528
Own Kudos [?]: 257 [0]
Given Kudos: 0
Location: USA
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 15:25
Sunshine,

allabout is right.

Either you have to take all three variables as 2L or L.

I just assumed the crossing point as the front of the first train to end of the same train. In this case the length is L

If you assume the crossing point as complete length of 2 trains the it should be 2L in all of the equations.

HTH.
User avatar
SunShine
Manager
Manager
Joined: 11 Nov 2005
Posts: 129
Own Kudos [?]: 54 [0]
Given Kudos: 0
Location: London
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 15:33
Thanks, giddi77, Now it is clear.....

In general the lenght is always L+L either travelling in one direction or opposite.
But the speed is S1+S2 when travelling in opposite direction and S1-S2 0r S2-S1 when travelling in the same direction.......

please correct me if wrong!


giddi77 wrote:
Sunshine,

allabout is right.

Either you have to take all three variables as 2L or L.

I just assumed the crossing point as the front of the first train to end of the same train. In this case the length is L

If you assume the crossing point as complete length of 2 trains the it should be 2L in all of the equations.

HTH.
User avatar
hkm_gmat
Manager
Manager
Joined: 05 Jan 2005
Posts: 132
Own Kudos [?]: 24 [0]
Given Kudos: 0
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 18:41
allabout wrote:
hkm_gmat wrote:
Good Question , keep them coming. Let us know the source.

Ans D

Let
L be the length of the Train
S be the speed of the slow Train
F be the speed of the fast Train


We have :

1. 2L/(F+S) = T

2. 2L/(F-S) = t

solving 1 & 2

F = L(t+T)/tT

we need to find 2L/F

= 2tT/T+t


It aren't two "lenghts" but one length that is passed by a train with speed s1+s2. In case this is unclear: Imagine two trains cross each other; they actually don't pass two lengths but one in a faster time.

Maybe this hint is useless or idle, but maybe it is helpful for other questions.
However in this case it doesn't matter since you use two lenghts in both statement 1 and 2.


Since the Trains completely pass each other the distance ought to be two times length of each train or 2L .
User avatar
giddi77
Director
Director
Joined: 21 Sep 2003
Posts: 528
Own Kudos [?]: 257 [0]
Given Kudos: 0
Location: USA
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   06 Jan 2006, 19:39
hkm_gmat wrote:
allabout wrote:
hkm_gmat wrote:
Good Question , keep them coming. Let us know the source.

Ans D

Let
L be the length of the Train
S be the speed of the slow Train
F be the speed of the fast Train


We have :

1. 2L/(F+S) = T

2. 2L/(F-S) = t

solving 1 & 2

F = L(t+T)/tT

we need to find 2L/F

= 2tT/T+t


It aren't two "lenghts" but one length that is passed by a train with speed s1+s2. In case this is unclear: Imagine two trains cross each other; they actually don't pass two lengths but one in a faster time.

Maybe this hint is useless or idle, but maybe it is helpful for other questions.
However in this case it doesn't matter since you use two lenghts in both statement 1 and 2.


Since the Trains completely pass each other the distance ought to be two times length of each train or 2L .


Sorry hkm_gmat, I completely missed your post. You are right, 2L can also be taken if we assume that the trian cross completely.

IMO, the problem doesn't depend on whether you consider the length as L or 2L. In all three cases the relative speed/velocity is what is varying.
User avatar
krisrini
Manager
Manager
Joined: 15 Apr 2005
Posts: 159
Own Kudos [?]: 32 [0]
Given Kudos: 0
Location: India, Chennai
Send PM
Re: Two trains cross each other in time T, when they are [#permalink] New post   08 Jan 2006, 21:49
Very good discussion on this post. The Oa is 2Tt/(T+t). NO OE was given.Thanks for all your replies.

regards



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Two trains cross each other in time T, when they are [#permalink]
08 Jan 2006, 21:49
Moderators:
Bunuel
Math Expert
92959 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions