It is currently 21 Sep 2017, 03:46

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

John and Karen begin running at opposite ends of a trail unt

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
MBA Section Director
User avatar
P
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4635

Kudos [?]: 3624 [1], given: 2404

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
GMAT ToolKit User Premium Member
John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Sep 2013, 12:16
1
This post received
KUDOS
Expert's post
22
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

60% (02:24) correct 40% (02:32) wrong based on 401 sessions

HideShow timer Statistics

A Nice Question from VERITAS.
OA and OE will be posted after few responses. Brief and Correct explanations will be rewarded with a Kudo.



John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

A) 25%
B) 50%
C) 75%
D) 100%
E) 200%

Happy Solving!
[Reveal] Spoiler: OA

_________________

Every Wednesday: Meet MBA Experts in Chat Room and Ask Your Most-Pressing MBA Admission Questions to them in a Live Chat.

Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates


Last edited by Bunuel on 04 Sep 2013, 07:28, edited 1 time in total.
Added the OA.

Kudos [?]: 3624 [1], given: 2404

2 KUDOS received
Manager
Manager
avatar
Joined: 06 Jul 2013
Posts: 105

Kudos [?]: 34 [2], given: 42

GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
Reviews Badge
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Sep 2013, 20:55
2
This post received
KUDOS
if john speed is S then Karen is 1.5S
D = 1.5ST + ST
D= 2.5ST
where t is the time taken by each runner in normal case.
Now john only travel .25D so Karen has to travel .75D to meet him

.75D/1.5D = 1.25t
so she needs to travel 25% more time than usual time.
A

Kudos [?]: 34 [2], given: 42

1 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 727

Kudos [?]: 832 [1], given: 724

Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Sep 2013, 21:54
1
This post received
KUDOS
Narenn wrote:
A Nice Question from VERITAS.
OA and OE will be posted after few responses. Brief and Correct explanations will be rewarded with a Kudo.



John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

A) 25%
B) 50%
C) 75%
D) 100%
E) 200%

Happy Solving!


Took some time to understand the Q.

Here is my Solution.

Let distance be John and Karen by 90 Kms
John's speed: 10 km/hr ---Time taken: 9 hrs
Karen's speed: 15Km/hr, time taken : 6 hrs

Now if both are running at their constant speed then they will meet in 3 hrs 36 minutes (See below)

at 0 hrs ---Distance between the 2 is 90 kms
after 1 hrs: 65 Km
After 2 hrs : 40 kms
After 3 : 15 kms


In 1 hr distance covered by the 2 jointly is 25 kms so 15 kms will be covered in 15/25*60----> 36 minutes

At the meeting point Distance covered by John : 36 Kms and by Karen: 54 Kms
Now John covered on D/4 distance ie. 22.5 Km distance and thus Karen would have to travel the extra distance of 13.5 kms.
To cover 13.5 kms----> Karen would need 54 mins (13.5/15*60---- 54 minutes)
So Total time taken by Karen : 3 hrs 36 minutes+ 54 minutes----> 4.5 hrs or 9/2 hrs
Usual time: 3hr 36 minutes -----> 18/5 hrs

Hence % More ((9/2-18/5) / 18/5 )*100-----> 25%
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 832 [1], given: 724

5 KUDOS received
Intern
Intern
avatar
Joined: 31 Jan 2013
Posts: 17

Kudos [?]: 55 [5], given: 18

Schools: ISB '15
WE: Consulting (Energy and Utilities)
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Sep 2013, 22:59
5
This post received
KUDOS
Consider d1+d2 =d ( d1 = distance run by John and d2 = distance run by Karen)

d1:d2 = Js*T:(3/2)Js*T = 2:3 = 0.4d : 0.6d

Since the John stops after 25% run d1:d2 = 0.25d : 0.75d

Hence the % longer K needs to run is = 0.75-0.6/0.6 = 25%

/SM

Kudos [?]: 55 [5], given: 18

Expert Post
4 KUDOS received
MBA Section Director
User avatar
P
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4635

Kudos [?]: 3624 [4], given: 2404

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
GMAT ToolKit User Premium Member
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 04 Sep 2013, 06:35
4
This post received
KUDOS
Expert's post
Thank You so much for your responses and explanations.

Here is the Official Explanation from the VERITAS

Choice A.

If John covered 25% of the course before stopping, that means that Karen covered 75% of it. But she should have only had to run 60% of it – that’s because she runs 3 miles for every 2 that John runs (covering 50% more distance in the same amount of time), so she should have covered 3/5 of the territory. So then you can use the Percent Change calculation:

\(\frac{(75-60)}{60} = \frac{1}{4} = 25%\)

A is therefore the correct answer.
_________________

Every Wednesday: Meet MBA Experts in Chat Room and Ask Your Most-Pressing MBA Admission Questions to them in a Live Chat.

Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates

Kudos [?]: 3624 [4], given: 2404

Manager
Manager
avatar
Joined: 11 Aug 2012
Posts: 127

Kudos [?]: 132 [0], given: 16

Schools: HBS '16, Stanford '16
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 06 Sep 2013, 09:22
AMITAGARWAL2 wrote:
if john speed is S then Karen is 1.5S
D = 1.5ST + ST
D= 2.5ST
where t is the time taken by each runner in normal case.
Now john only travel .25D so Karen has to travel .75D to meet him

.75D/1.5D = 1.25t
so she needs to travel 25% more time than usual time.
A


Could someone explain in more detail this approach?

I don't understand its last division: .75D/1.5D = 1.25t
Where did he or she get 1.5D as divisor? :s

Thanks!

Kudos [?]: 132 [0], given: 16

5 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 466

Kudos [?]: 192 [5], given: 134

Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 09 Sep 2013, 04:17
5
This post received
KUDOS
1
This post was
BOOKMARKED
John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.

If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.

ANSWER: A) 25%

Kudos [?]: 192 [5], given: 134

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 382

Kudos [?]: 388 [0], given: 73

Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
GMAT ToolKit User
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 20 Nov 2013, 10:11
1
This post was
BOOKMARKED
Let john's speed=2 then karen's speed=(3/2)*2=3
Let total distance=40 then johns distance=(1/4)*40=10. Karens distance=30

Karens time=30/3=10hours
If everything were ok, then these guys would have met in 8 hours
40/(3+2)=8h

So, (10-8)/8*100%=25%
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Kudos [?]: 388 [0], given: 73

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17583

Kudos [?]: 270 [0], given: 0

Premium Member
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 21 Nov 2014, 09:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Manager
Manager
avatar
Joined: 22 Aug 2014
Posts: 190

Kudos [?]: 10 [0], given: 49

Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 14 May 2015, 01:18
WholeLottaLove wrote:
John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.

If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.

ANSWER: A) 25%



Very nice explanation.
Thanks a lot.Its easy to assume values.
:)

Kudos [?]: 10 [0], given: 49

3 KUDOS received
Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 801

Kudos [?]: 224 [3], given: 10

Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 20 Aug 2015, 20:17
3
This post received
KUDOS
Karen normally covers 3/5 of the distance.
Now she has to cover 3/4 of the distance.
3/4 / 3/5 = 1.25

Kudos [?]: 224 [3], given: 10

Intern
Intern
avatar
Joined: 16 Aug 2015
Posts: 27

Kudos [?]: 12 [0], given: 15

Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 510 Q22 V19
GPA: 3.41
GMAT ToolKit User
John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 23 Aug 2015, 06:45
Let's say total distance between Johm & Karen is 100 miles when they start.
If John would not have stopped then John & Karen would have approached each other at S+1.5S = 2.5S speed and met each other after time T hours and total distance by both have them would have covered = 100 miles.

Hence T = 100/2.5S

In Time T, distance covered by Karen at 1.5S speed is : 1.5S * 100/2.5S = 60 miles.
Hence Karen would have covered 60 miles to meet John if John would not have stopped.

Given that John stopped after covering 25 miles means Karen covered 75 miles.


% = (75-60) * 100 / 60 = 25% Ans.

Kudos [?]: 12 [0], given: 15

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17583

Kudos [?]: 270 [0], given: 0

Premium Member
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 30 Sep 2016, 05:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Intern
Intern
avatar
B
Joined: 16 Sep 2015
Posts: 4

Kudos [?]: [0], given: 451

CAT Tests
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 01 Oct 2016, 09:13
the wording is a bit confusing. you can change it to 25% of the total distance. i took to be 25% of his normal distance before they met.

Kudos [?]: [0], given: 451

2 KUDOS received
Intern
Intern
User avatar
B
Joined: 28 Mar 2016
Posts: 17

Kudos [?]: 12 [2], given: 13

Location: United States (UT)
Reviews Badge
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 02 Oct 2016, 21:07
2
This post received
KUDOS
Skip the math. 1st recognize that the answer choices are far apart and thus, this is a probaby a perfect problem to estimate.

*IF* Karen and John ran at the same rate, then they would have met at 50% mark. But since John is a wimp who can't push through his cramps ;) Karen now has to run 50% farther (to reach John who's sitting at 25%)...

BUT remember that Karen actually runs faster than wimpy old John, so they would have met somewhere closer to Johns starting point had John not quit. But he did quit, so we know that Karen is going to have to run <50% farther to reach crying John.

Thus Answer A is the only available option.

Posted from my mobile device

Kudos [?]: 12 [2], given: 13

1 KUDOS received
Manager
Manager
avatar
S
Joined: 14 Oct 2012
Posts: 150

Kudos [?]: 42 [1], given: 906

Premium Member Reviews Badge CAT Tests
Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 26 Jan 2017, 13:14
1
This post received
KUDOS
My 2 cents,
Karen’s speed = 1.5 * John’s speed = 3/2 * John’s speed.
Therefore, Sk = 3 mph and Sj = 2 mph.
Total distance = 60 miles (3*2*10)
Sk/Sj = dk/dj = 3/2 => dk/D = 3/5 & dj/D = 2/5
Therefore, dk = 60 * 3/5 = 36 miles.
Total time taken T (would be sum of speeds of BOTH Karen and John);
T = D/(Sk + Sj) = 60/5 = 12 hrs.

Now, as John stops at 25% of distance due to cramps;
Karen has to cover 75% of distance = ¾ * 60 = 45 miles.
Therefore, % increase of distance covered by Karen
= (New - Old)/Old * 100 = (45 – 36)/36 * 100 = 9/36* 100 = ¼ * 100 = 25% | A

If my post was helpful to you, please kudo :idea:

Kudos [?]: 42 [1], given: 906

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 91

Kudos [?]: 6 [0], given: 22

John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 02 Aug 2017, 16:32
I think the trick of this question is instantly plugging in made up values.

Also knowing you can add rates together. For instance if I am driving at 50KM an hour and you're driving at 50 and we're both driving at eachother the actual speed is 100KM of the gap we're closing.

So if there is 100KM between us and we're both moving at 50KM we would meat eachother in 1 hour as our total speed is 100KM. D=RT 100 = 100 T. So this knowledge helps
Attachments

V Q, 19.png
V Q, 19.png [ 266.69 KiB | Viewed 606 times ]

Kudos [?]: 6 [0], given: 22

Manager
Manager
avatar
B
Joined: 07 Jun 2017
Posts: 111

Kudos [?]: 3 [0], given: 452

Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Aug 2017, 00:08
AMITAGARWAL2 wrote:
if john speed is S then Karen is 1.5S
D = 1.5ST + ST
D= 2.5ST
where t is the time taken by each runner in normal case.
Now john only travel .25D so Karen has to travel .75D to meet him

.75D/1.5D = 1.25t
so she needs to travel 25% more time than usual time.
A


Dear,
Why do you divided 0.75D by 1.5 D?
I don't understand the 1.5 D part.

Thank you so much.

Kudos [?]: 3 [0], given: 452

Manager
Manager
avatar
B
Joined: 07 Jun 2017
Posts: 111

Kudos [?]: 3 [0], given: 452

Re: John and Karen begin running at opposite ends of a trail unt [#permalink]

Show Tags

New post 03 Aug 2017, 01:51
Smallwonder wrote:
Consider d1+d2 =d ( d1 = distance run by John and d2 = distance run by Karen)

d1:d2 = Js*T:(3/2)Js*T = 2:3 = 0.4d : 0.6d

Since the John stops after 25% run d1:d2 = 0.25d : 0.75d

Hence the % longer K needs to run is = 0.75-0.6/0.6 = 25%

/SM


Dear,

I don't understand this part --> Js*T:(3/2)Js*T = 2:3 = 0.4d : 0.6d
Would you explain what is Js*T? Thank you

Kudos [?]: 3 [0], given: 452

Re: John and Karen begin running at opposite ends of a trail unt   [#permalink] 03 Aug 2017, 01:51
    Similar topics Author Replies Last post
Similar
Topics:
55 EXPERTS_POSTS_IN_THIS_TOPIC Two trains run in opposite directions on a circular track. alex1233 27 30 Aug 2017, 12:42
6 EXPERTS_POSTS_IN_THIS_TOPIC Points A and B are at opposite ends of a circular pond with Revenge2013 4 17 Mar 2017, 03:20
46 EXPERTS_POSTS_IN_THIS_TOPIC Two trains started simultaneously from opposite ends of a Madelaine88 12 02 Apr 2016, 18:29
7 EXPERTS_POSTS_IN_THIS_TOPIC John is a trail runner who decides to take a day off work to run up Gnpth 4 04 Aug 2017, 20:19
19 EXPERTS_POSTS_IN_THIS_TOPIC John and Amanda stand at opposite ends of a straight road and start Bunuel 13 20 Mar 2017, 02:38
Display posts from previous: Sort by

John and Karen begin running at opposite ends of a trail unt

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.