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Two trains cross each other in time T, when they are [#permalink]
05 Jan 2006, 03:25

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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?

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 _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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.

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

Re: PS - Relative velocity [#permalink]
06 Jan 2006, 14:16

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?

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. _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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.

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 .

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. _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."