An algebra problem by Kartik Bhide

Algebra Level 1

Artik and Bide are positioned in two cars that are 100 kilometers apart on a straight road. If they both travel in the same direction, then they will meet in 5 hours. If however, they travel towards each other, then they will meet in 1 hour. Let \(u\) and \(v\) be the speeds (in km/hr) of Artik's and Bide's car respectively. Find \[\frac{u-v}{2}.\]

Note: \(u > v\)

Image credit: Wikipedia Lionel Allorge
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