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Found problems: 1

2006 ISI B.Math Entrance Exam, 6
Tags: number theory theorems , calculus
You are standing at the edge of a river which is $1$ km wide. You have to go to your camp on the opposite bank . The distance to the camp from the point on the opposite bank directly across you is $1$ km . You can swim at $2$ km/hr and walk at $3$ km-hr . What is the shortest time you will take to reach your camp?(Ignore the speed of the river and assume that the river banks are straight and parallel).