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

Given:
1. John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points.
2. They each run at their respective constant rates until John gets a cramp and stops.

Asked: 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.

vK / vJ = 1.5

Let the speeds of John and Karen be 2x & 3x mph respectively

Let the length of the trail be L miles

Normal Case:
Distance = L miles
Relative speed = 2x + 3x = 5x mph
Time taken to meet = L/5x= .2L/x hours

Abnormal Case : John is only able to cover 25% of the distance before he stops
Time when both were running = (L/4)/5x = L/20x hours
Distance covered by both in L/20x hours = L/20x * (2x + 3x) = L/4

Remaining distance = 3L/4
Time taken by Karen to cover 3L/4 distance = 3L/4 /(3x) = L/4x

Total time run by Karen = L/20x + L/4x = 6L/20x = 3L/10x = .3L/x

Extra time run by Karen = .3L/x - .2L/x = .1L/x

Percent longer would Karen have run ={ (.1L/x)/(.2L/x)}*100% = 50%

IMO B

Bunuel
I think OA should be B
Please check whether OA is correct.

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%