# John and Karen

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%

Expert Asked on March 27, 2018 in

There are multiple approaches to work out this problem. The easiest way is to use numbers to work out things faster. Also whenever two objects are moving, you can make use of the concept of relative speed.

Let John’s speed = 2m/hr then Karen’s speed = (3/2)*2 = 3m/hr

Let total distance = 40 (multiple of 4 since we have 25% and 75%) Then Johns distance = (1/4)*40 = 10miles and Karen’s distance = 30miles

Actual time Taken by Karen when John stopped = 30/3 = 10hours

If everything went to plan, then both Karen and John would have met in Distance/Relative Speed = 40/(3+2) = 8hours (the relative speed is the addition of the two speeds since they are moving towards each other)

= (10-8)/8 = 25%

Hope this helps!

Expert Answered on April 20, 2018.