Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 26 Feb 2011
Posts: 29

Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
Updated on: 27 Jun 2013, 02:14
Question Stats:
78% (02:10) correct 22% (02:25) wrong based on 660 sessions
HideShow timer Statistics
Two trains started simultaneously from opposite ends of a 100mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100mile trip in 5 hours; train Y, travelling at a constant rate, completed the 100mile trip in 3 hours. How many miles had X traveled when it met train Y? A. 37.5 B. 40.0 C. 60.0 D. 62.5 E. 77.5
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Madelaine88 on 02 Mar 2011, 06:18.
Last edited by Bunuel on 27 Jun 2013, 02:14, edited 2 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 59125

Re: 2 trains
[#permalink]
Show Tags
02 Mar 2011, 06:39
Madelaine88 wrote: Two trains started simultaneously from opposite ends of a 100mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100mile trip in 5 hours; train Y, travelling at a constant rate, completed the 100mile trip in 3 hours. How many miles had X traveled when it met train Y?
A/ 37.5 B/ 40.0 C/ 60.0 D/ 62.5 E/ 77.5 As the ratio of the rates of X and Y is 3 to 5 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 3/(3+5)=3/8 of 100 miles: 100*3/8=37.5 miles. Answer: A.
_________________




Senior Manager
Joined: 17 Sep 2013
Posts: 320
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
19 Sep 2013, 05:00
Speed of first train: 100/5 = 20 Mph Speed of second train: 100/3 = 33.33 Mph Now in 1 hr distance covered by X is 20 & that by Y is 33.33.In the next hr it will be 40 & 66.66 resp. 40+66.66=106.6> the distance between them...So they would have met by now & the answer would be something less than 40..which leaves us with A
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..




Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 647

Re: 2 trains
[#permalink]
Show Tags
02 Mar 2011, 06:30
Train X : 100 m in 5 hrs speed = 100/5 = 20mph Train Y : 100 m in 3 hrs speed = 100/3 mph
The distance shrinking at effective speed (20 + 100/3 ) mph Time of intersect = 100 / (20+100/3) = 15/8 hrs Distance travelled by X < Distance travelled by Y
Distance travelled by X = time * speed = 15/8 * 20 = 75/2



Manager
Joined: 15 Apr 2011
Posts: 59

Re: 2 trains
[#permalink]
Show Tags
13 Apr 2012, 00:42
Bunuel, could you please explain this. It is not clear to me. thanks!
_________________
http://mymbadreamz.blogspot.com



Manager
Joined: 13 Mar 2012
Posts: 198
Concentration: Operations, Strategy

Re: 2 trains
[#permalink]
Show Tags
13 Apr 2012, 02:02
vel x/ vel y=3/5 let they met after t time, distance travelled by X=x then, x/vel x=(100x)/ vel y => x/(100x)= 3/5 => x= 300/8= 37.5
_________________
Practice Practice and practice...!!
If my reply /analysis is helpful>please press KUDOS If there's a loophole in my analysis> suggest measures to make it airtight.



Math Expert
Joined: 02 Sep 2009
Posts: 59125

Re: 2 trains
[#permalink]
Show Tags
13 Apr 2012, 02:12
mymbadreamz wrote: Bunuel, could you please explain this. It is not clear to me. thanks! Since, the ratio of times of X and Y to cover the same distance of 100 miles is is 5:3, then the ratio of their rates is 3:5. Consider this, say the rates of trains X and Y are X and Y respectively, then: Distance=Rate*Time > X*5=Y*3 > ratio of the rates is X:Y=3:5. At the time they meet, so after they travel the same time interval the ratio of distances covered by X and Y would also be in that ratio (for example if X=3 mph and Y=5 mph then they would meet in 100/(3+5)=100/8 hours, hence train X would cover 300/8 miles and train Y would cover 500/8 miles > ratio of distances covered (300/8):(500/8)=3:5). Now, since the the ratio of distances covered by X and Y is 3:5 then X covered 3/(3+5)=3/8 of the total distance. Hope it's clear.
_________________



Manager
Joined: 13 Jul 2013
Posts: 61

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
19 Sep 2013, 02:37
Why is that when the meet they would have covered 100 miles? This bit is little confusing.



Math Expert
Joined: 02 Sep 2009
Posts: 59125

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
19 Sep 2013, 04:55
theGame001 wrote: Why is that when the meet they would have covered 100 miles? This bit is little confusing. When they meet one train covers some part of 100mile distance and another covers the remaining part of 100mile distance, so combined they cover 100 miles.
_________________



Intern
Joined: 04 May 2015
Posts: 2

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
30 Dec 2015, 10:48
Speed of train X= Distance/Time = 100/5 = 20 mph
Speed of train Y= Distance/Time = 100/3 = 33.33 mph
Relative Speed (opposite direction) = 20+33.33 = 53.33 mph
Now, Time when X & Y meet:
Distance = Relative Speed x Time
Time= D/RS = 100/53.33 = 1.87 hrs
After 1.87 hrs X & Y meet at some distance
In 1.87 hrs, X traveled
Distance= 20 x 1.87 =37.50 miles (Answer)
And Y traveled,
Distance= 33.33 x 1.87 = 62.3 (approx.)
Answer is A.
I hope it makes your life somewhere easy. Hit kudos if like.



Manager
Joined: 17 Nov 2013
Posts: 77

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
02 Apr 2016, 18:29
RxT = D. D/R = T, SO WHEN YOU SEE TIME = 100 AND THE CHALLENGE IS THAT BOTH TRAINS MUST MEET SO YOU NEED TO ADD (+) THE INDIVIDUAL RATES. ALSO, TO GET THE INDIVIDUAL RATES USE FOR X = 100/5 = 20 M/H, RATE FOR Y = 100/3 M/H. SO IN YOUR FORMULA YOU HAVE: \(\frac{100}{(20+(100/3))} = T\) => T = 15/8, MEANING BOTH TRAINS MET AT 15/8 TIME. TO FIND OUT THE DISTANCE AT WHICH X MET Y, YOU DO R x T = D => 20 x (15/8) => D = 37.5 MILES FOR X WHET IT MET Y.



VP
Joined: 09 Mar 2016
Posts: 1229

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
11 Apr 2018, 04:49
Bunuel wrote: Madelaine88 wrote: Two trains started simultaneously from opposite ends of a 100mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100mile trip in 5 hours; train Y, travelling at a constant rate, completed the 100mile trip in 3 hours. How many miles had X traveled when it met train Y?
A/ 37.5 B/ 40.0 C/ 60.0 D/ 62.5 E/ 77.5 As the ratio of the rates of X and Y is 3 to 5 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 3/(3+5)=3/8 of 100 miles: 100*3/8=37.5 miles. Answer: A. Hello Bunuel can you please advise if my approach is correct Speed X = 100/5= 20 Speed y = 100/3 = 33.33 relative speed 20+33 =53 time when they meet = 100/53 =1.8 Distance done by X when meeting Y > 20*1.8 = 36 (I got approximate answer , is it correct ? ) thank you!



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3568

Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
11 Apr 2018, 05:19
dave13 wrote: Hello Bunuel can you please advise if my approach is correct Speed X = 100/5= 20 Speed y = 100/3 = 33.33 relative speed 20+33 =53 time when they meet = 100/53 =1.8 Distance done by X when meeting Y > 20*1.8 = 36 (I got approximate answer , is it correct ? ) thank you! Hey dave13 , Yes, your approach is 100% correct. If you get the time to two decimal places, you will get more closer answer to 37.5. Thanks!
_________________
My LinkedIn abhimahna.My GMAT Story: From V21 to V40My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeBlog: Subscribe to Question of the Day BlogGMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club!Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 732
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
12 Apr 2018, 10:24
dave13 wrote: Bunuel wrote: Madelaine88 wrote: Two trains started simultaneously from opposite ends of a 100mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100mile trip in 5 hours; train Y, travelling at a constant rate, completed the 100mile trip in 3 hours. How many miles had X traveled when it met train Y?
A/ 37.5 B/ 40.0 C/ 60.0 D/ 62.5 E/ 77.5 As the ratio of the rates of X and Y is 3 to 5 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 3/(3+5)=3/8 of 100 miles: 100*3/8=37.5 miles. Answer: A. Hello Bunuel can you please advise if my approach is correct Speed X = 100/5= 20 Speed y = 100/3 = 33.33 relative speed 20+33 =53 time when they meet = 100/53 =1.8 Distance done by X when meeting Y > 20*1.8 = 36 (I got approximate answer , is it correct ? ) thank you! dave13 Perfect approach .Relative speed concept is used nicely with proper simplification of numbers. However if you keep the relative speed as is: 100 ( 1/5 + 1/3 ) = 100*8/15 (Speed) time = 100/(100*8/15) = 15/8 hr distance traveled by 20*15/8 = 75/2 = 37.5 It would help if the options were very close. Supposed we have 36 & 37.5 both in the options... Best, Gladi
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)



Senior Manager
Joined: 15 Jan 2017
Posts: 334

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
30 Jul 2018, 23:25
Solved it this way: train x: 100/5 = 20 mph train y: 100/ 3 = 33.4 mph (approx) relative speed = 100/53.4 = 25/13.1 = approx 2 hours so time for X > 20mph*2 = 40 > but since its not actually 2 hours but close to it, it must closer to 40 not 40. Which is option A) 37.5 Kudos if you liked this solution



Intern
Joined: 16 May 2017
Posts: 48
GPA: 3.8
WE: Medicine and Health (Health Care)

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
20 Oct 2018, 02:29
Train X travelling speed= 100/5 mph Train Y travelling speed=100/3 mph Relative speed as they are travelling in opposite direction= 100/5+100/3= 800/15 mph
Time after which X and Y would meet= distance/relative speed= 100/800/15= 100*15/800= 15/8 hr
X travelled distance when it met with train Y= speed*time they met= 100*15/5*8= 37.5 miles.
Ans (A)



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8412
Location: United States (CA)

Re: Two trains started simultaneously from opposite ends of a
[#permalink]
Show Tags
09 Sep 2019, 10:58
Madelaine88 wrote: Two trains started simultaneously from opposite ends of a 100mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100mile trip in 5 hours; train Y, travelling at a constant rate, completed the 100mile trip in 3 hours. How many miles had X traveled when it met train Y?
A. 37.5 B. 40.0 C. 60.0 D. 62.5 E. 77.5 The combined distance traveled by the two trains was 100 miles. Each train traveled for t hours. We can create the distance equation: 100/5 * t + 100/3 * t = 100 Multiplying by 15 to clear the fractions from the equation, we have: 300t + 500t = 1500 800t = 1500 t = 15/8 Thus, train X had traveled 15/8 x 100/5 = 15/8 x 20 = 37.5 miles by the time it reached Y. Answer: A
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: Two trains started simultaneously from opposite ends of a
[#permalink]
09 Sep 2019, 10:58






