Problem solving - RTD question. Need Help!!

[Prernasrk]

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%

[s.vishnu]

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]

[Prernasrk]

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

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]

[Prernasrk]

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

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

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]

[s.vishnu]

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.

[GMATGuruNY]

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.