Trains

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gmat7202011: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sat Dec 11, 2010 2:39 pm; Thanked: 3 times

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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Source: Beat The GMAT — Problem Solving | Thu Dec 23, 2010 7:03 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

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.

Thanks
Anshu

(Every mistake is a lesson learned )

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

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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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

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.

Thanks
Anshu

(Every mistake is a lesson learned )

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gmat7202011: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sat Dec 11, 2010 2:39 pm; Thanked: 3 times

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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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

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).

Thanks
Anshu

(Every mistake is a lesson learned )

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

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.

Rahul Lakhani
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Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)

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