BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Relative Speeds - gmatclub

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

Relative Speeds - gmatclub

by rohu27 » Thu Mar 24, 2011 9:39 pm
Make sure you time this while doing!! Good one.


Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

(A) 0
(B) 30 miles
(C) 60 miles
(D) 90 miles
(E) 120 miles


[spoiler]OA : B[/spoiler]
Last edited by rohu27 on Thu Mar 24, 2011 10:47 pm, edited 1 time in total.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Thu Mar 24, 2011 9:47 pm
Let L be the distance from washington at first meet.
L = after 1 hour trains meet 30mile from washington

M be second meet = After 2hr train train B travels 180 mile(in total) and train B travel 60mile from washington

L-M = 60-30 =30

B for me
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Thu Mar 24, 2011 10:37 pm
Agree with HSPA.

OA Please.

Is there any other way to do it ?
Top
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

by rohu27 » Thu Mar 24, 2011 10:53 pm
OA is indeed B.
I solved using the traditional approach.

to calculate the first meeting point, t=120/90+30 = 1 (they wud meet after 1 hour)
so at 30 miles frm washington.

train B reaches desination washinton and starts for B again(this when the second meeting would happen)
train B reaches Washington in 4/3 hrs. distance travleld by A in 4/3 hrs=40miles.
so time taken for the second meet = 40/90-30=2/3.
distance=2/3*90=60

total distance travlled =90-60=30miles.
Top
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

by rohu27 » Thu Mar 24, 2011 10:56 pm
HSPA wrote: M be second meet = After 2hr train train B travels 180 mile(in total) and train B travel 60mile from washington

L-M = 60-30 =30

B for me
HSPA,
how can we be sure that the second meeting will also happen after an hour? confused :(
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Thu Mar 24, 2011 11:27 pm
rohu27 wrote:
HSPA wrote: M be second meet = After 2hr train train B travels 180 mile(in total) and train B travel 60mile from washington

L-M = 60-30 =30

B for me
HSPA,
how can we be sure that the second meeting will also happen after an hour? confused :(
Good doubt rohu. Can somebody pls split open this question so that we can deal with them with a particular approach in mind.
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 65
Joined: Mon Mar 07, 2011 12:27 am
Thanked: 6 times

by 6983manish » Thu Mar 24, 2011 11:31 pm
rohu27 wrote:
HSPA wrote: M be second meet = After 2hr train train B travels 180 mile(in total) and train B travel 60mile from washington

L-M = 60-30 =30

B for me
HSPA,
how can we be sure that the second meeting will also happen after an hour? confused :(
Relative speed = 90+30 = 120 km/hr as both the trains are traveling in opposite directions.

For first time meet up , total time consumed would be = 120Km /120 kmph = 1hr

Train A reaches Baltimore and then turn back to Washington and train B does the vice versa . Hence they cover another 120 Hrs in 1 Hr. ( Distance is still same = 120Km ).

Hope this clarifies , "why they meet up after an hour ?".
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Thu Mar 24, 2011 11:48 pm
Train A reaches Baltimore and then turn back to Washington and train B does the vice versa . Hence they cover another 120 Hrs in 1 Hr. ( Distance is still same = 120Km ).
Hi Manish, U are confusing me further:

For train A to reach Baltimore it will take 4 hours since it travels at a speed of 30mph & the distance is 120 & what i infer from the information given is that Before the train A reaches Baltimore A & B will have met 2nd time already.

Does my logic makes any sense.
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 65
Joined: Mon Mar 07, 2011 12:27 am
Thanked: 6 times

by 6983manish » Thu Mar 24, 2011 11:58 pm
ankur.agrawal wrote:
Train A reaches Baltimore and then turn back to Washington and train B does the vice versa . Hence they cover another 120 Hrs in 1 Hr. ( Distance is still same = 120Km ).
Hi Manish, U are confusing me further:

For train A to reach Baltimore it will take 4 hours since it travels at a speed of 30mph & the distance is 120 & what i infer from the information given is that Before the train A reaches Baltimore A & B will have met 2nd time already.

Does my logic makes any sense.
Hi Ankur

Yes , your logic makes sense.

Train B will meet train A again while A moving to Baltimore.

Thanks
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Fri Mar 25, 2011 12:11 am
Hope this clarifies , "why they meet up after an hour ?".

So the Question by Rohu is still open.
Top
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

by rohu27 » Fri Mar 25, 2011 12:15 am
Ankur, if u see my explanation, no assumptions to be made or rather no logic used as such, we can arrive at the answer purely on the basis of math.

may take some time though.


ankur.agrawal wrote:Hope this clarifies , "why they meet up after an hour ?".

So the Question by Rohu is still open.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Fri Mar 25, 2011 12:24 am
rohu27 wrote:Ankur, if u see my explanation, no assumptions to be made or rather no logic used as such, we can arrive at the answer purely on the basis of math.

may take some time though.


ankur.agrawal wrote:Hope this clarifies , "why they meet up after an hour ?".

So the Question by Rohu is still open.
Yes rohu. your solution is absolutely full proof . I was just seeking out the alternate explanations, if any?

Thanks.
Top
Legendary Member
Posts: 586
Joined: Tue Jan 19, 2010 4:38 am
Thanked: 31 times
Followed by:5 members
GMAT Score:730

by rohu27 » Fri Mar 25, 2011 12:29 am
we can wait for HSPA to respond.tht was real quick in just 2steps.

ankur.agrawal wrote:
rohu27 wrote:Ankur, if u see my explanation, no assumptions to be made or rather no logic used as such, we can arrive at the answer purely on the basis of math.

may take some time though.


ankur.agrawal wrote:Hope this clarifies , "why they meet up after an hour ?".

So the Question by Rohu is still open.
Yes rohu. your solution is absolutely full proof . I was just seeking out the alternate explanations, if any?

Thanks.
Top
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Fri Mar 25, 2011 1:01 am
Train A speed = 30 miles/ hour and it need to travel for 120Km
So this will take 4 hours to reach destination Baltimore

First meet will happen when they are moving in opposite direction.. A towards baltimore and B towards washington
Second meet will happen when both are travelling in the same direction 60 miles from Baltimore

In two hours train B travels 180 miles = 120 Balti to washing + 60 miles washing to balti [ Here turn around times are neglible]
In two hours train A travels 60 miles frm washing to balti..

I calculated distance travelled in two hours. I never counted for the time of second meet
Top
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Fri Mar 25, 2011 1:06 am
Kindly ping Mitch Hunt(GMAT guru)... He is a teacher by profession.. I am doubting if my explanation is sufficent.

Mitch can you put down your words and approach for this.
Top
Post new topic Post Reply