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Trains

by gmat7202011 » Thu Dec 23, 2010 7:03 pm
Two trains A and B travel in the same direction from NY to DC

Train A starts at 6:00 AM at 98m/hr

Train B starts at 6:45 AM at 136m/hr

After travelling for what distance from NY will they meet.
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by anshumishra » Thu Dec 23, 2010 7:24 pm
gmat7202011 wrote:Two trains A and B travel in the same direction from NY to DC

Train A starts at 6:00 AM at 98m/hr

Train B starts at 6:45 AM at 136m/hr

After travelling for what distance from NY will they meet.
When train B starts, Train A has already travelled : 98*3/4 miles
Relative speed of Train B against Train A = 136-98 = 38 miles/hr

Time taken by Train B to cover the lead distance = (98*3/4)/38 hrs
So, the distance from NY where they meet = 136*(98*3/4)/38 miles ~= 263 miles (Based on Train B's Speed)
or
98*3/4[1+98/38] ~= 263 miles (Based on Train A's speed)
Last edited by anshumishra on Thu Dec 23, 2010 7:27 pm, edited 1 time in total.
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by diebeatsthegmat » Thu Dec 23, 2010 7:25 pm
gmat7202011 wrote:Two trains A and B travel in the same direction from NY to DC

Train A starts at 6:00 AM at 98m/hr

Train B starts at 6:45 AM at 136m/hr

After travelling for what distance from NY will they meet.
this doesnt make sense, how come they meet each other while they go toward the same dirrection from NY to DC?
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by anshumishra » Thu Dec 23, 2010 7:29 pm
diebeatsthegmat wrote:
gmat7202011 wrote:Two trains A and B travel in the same direction from NY to DC

Train A starts at 6:00 AM at 98m/hr

Train B starts at 6:45 AM at 136m/hr

After travelling for what distance from NY will they meet.
this doesnt make sense, how come they meet each other while they go toward the same dirrection from NY to DC?
Because the Second train, which leaves after the first train leaves, is fast and somewhere in between the trip it leaves the first train behind.
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by gmat7202011 » Thu Dec 23, 2010 7:45 pm
Thanks Anshu,

I got the concept that it has to break the lead of 98*(3/4). And it has to break traveling at a speed of 136.

So i get the time that it will take to break the distance as 98*(3/4)/38

However , the reason it has to be multiplied by 136 is, Train B will travel at a speed of 136m/hr for 98*(3/4)/38 hr so as to nullify the lead. Is my reasoning correct.

Thanks again
Last edited by gmat7202011 on Thu Dec 23, 2010 7:52 pm, edited 1 time in total.
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by anshumishra » Thu Dec 23, 2010 7:51 pm
gmat7202011 wrote:Thanks Anshu,

I got the concept that it has to break the lead of 98*(3/4). And it has to break traveling at a speed of 136.

So i get the time that it will take to break the distance as 98*(3/4)/38

However , the reason it has to be multiplied by 136 is, Train A will travel at a speed of 136m/hr for 98*(3/4)/38 hr so as to nullify the lead. Is my reasoning correct.

Thanks again
Exactly ! You are correct !
You can either find how far train B travelled during the time it took to nullify train A's lead
or
how far train A travelled before the train B took it over

I have mentioned both of the equations in my previous post, just to show that both approaches are fine (although first one is easier and faster here).
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by Rahul@gurome » Thu Dec 23, 2010 7:56 pm
gmat7202011 wrote:Thanks Anshu,

I got the concept that it has to break the lead of 98*(3/4). And it has to break traveling at a speed of 136.

So i get the time that it will take to break the distance as 98*(3/4)/38

However , the reason it has to be multiplied by 136 is, Train A will travel at a speed of 136m/hr for 98*(3/4)/38 hr so as to nullify the lead. Is my reasoning correct.

Thanks again
98*(3/4)/38 is the time in which B catches up with A.

During this time B has travelled at the speed of 136m/hr.
So the distance B has covered is 136*{98*(3/4)/38}.
This is also the distance from NY to DC.
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