Problem solving - RTD question. Need Help!! - The Beat The GMAT Forum

Problem solving - RTD question. Need Help!!

Expert replies

Prernasrk: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Aug 20, 2013 1:13 pm

by Prernasrk » Mon Oct 14, 2013 5:36 am

Can someone show me an easy way fo solving this?

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.

25%

50%

75%

100%

200%

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 14, 2013 5:36 am

s.vishnu: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jan 02, 2012 6:20 am; Thanked: 2 times

by s.vishnu » Mon Oct 14, 2013 7:15 am

Hi,
The question basically asks us how much more distance is Karen running now than would have ,had John not stopped running.

Assuming the distance between them to be 100units.

John covered 25 units => Karen has to cover 75 units now.

In case John ran at his constant speed,At the meeting point

Distance travelled by John/speed of John=Distance travelled by Karen/Speed of Karen

Assume x to be the distance travelled by John
=>100-x is the distance travelled by Karen

Given:Karen travels 1.5times faster than John

x/J=(100-x)/1.5J => x=40

100-x=60(distance travelled by Karen)

Percentage increase

[spoiler][75-60/60)*100=25%[/spoiler]

Is this the answer?

[spoiler][/spoiler][spoiler][/spoiler]

Like this post

Prernasrk: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Aug 20, 2013 1:13 pm

by Prernasrk » Mon Oct 14, 2013 7:26 am

Yes. Thats right...this was a much better explanation !!!...thanks

s.vishnu wrote:Hi,
The question basically asks us how much more distance is Karen running now than would have ,had John not stopped running.

Assuming the distance between them to be 100units.

John covered 25 units => Karen has to cover 75 units now.

In case John ran at his constant speed,At the meeting point

Distance travelled by John/speed of John=Distance travelled by Karen/Speed of Karen

Assume x to be the distance travelled by John
=>100-x is the distance travelled by Karen

Given:Karen travels 1.5times faster than John

x/J=(100-x)/1.5J => x=40

100-x=60(distance travelled by Karen)

Percentage increase

[spoiler][75-60/60)*100=25%[/spoiler]

Is this the answer?

[spoiler][/spoiler][spoiler][/spoiler]

Like this post

Prernasrk: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Aug 20, 2013 1:13 pm

by Prernasrk » Mon Oct 14, 2013 7:29 am

One question though.... why did you set up the below equation? it is no where said that the travel the same distance.

Distance travelled by John/speed of John=Distance travelled by Karen/Speed of Karen

Prernasrk wrote:Yes. Thats right...this was a much better explanation !!!...thanks
s.vishnu wrote:Hi,
The question basically asks us how much more distance is Karen running now than would have ,had John not stopped running.

Assuming the distance between them to be 100units.

John covered 25 units => Karen has to cover 75 units now.

In case John ran at his constant speed,At the meeting point

Distance travelled by John/speed of John=Distance travelled by Karen/Speed of Karen

Assume x to be the distance travelled by John
=>100-x is the distance travelled by Karen

Given:Karen travels 1.5times faster than John

x/J=(100-x)/1.5J => x=40

100-x=60(distance travelled by Karen)

Percentage increase

[spoiler][75-60/60)*100=25%[/spoiler]

Is this the answer?

[spoiler][/spoiler][spoiler][/spoiler]

Like this post

s.vishnu: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jan 02, 2012 6:20 am; Thanked: 2 times

by s.vishnu » Mon Oct 14, 2013 9:09 am

Your are welcome

At the point they met,the time duration for which both travelled would be the same as both began to run at the same time.

I hope this helps.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 14, 2013 12:34 pm

Prernasrk wrote:Can someone show me an easy way fo solving this?

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.

25%

50%

75%

100%

200%

Since Karen's rate is 50% faster than John's rate, for every 2 miles that John travels, the distance traveled by Karen = 2 + .5(2) = 3 miles.
Implication:
When Karen and John travel toward each other, of every 5 miles, 2 miles are traveled by John, while 3 miles are traveled by Karen.
Thus, of the total distance between Karen and John, the portion normally traveled by Karen = 3/5 = 60%.
When John gets a cramp, he travels only 25% of the total distance, implying that the portion traveled by Karen = 75%.
Percent increase from 60% to 75% = Difference/Original * 100 = 15/60 * 100 = 25%.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review