A man can swim 3 km / hr in still water. If the velocity of...

A man can swim $3 \mathrm{~km} / \mathrm{hr}$ in still water. If the velocity of the stream be $2 \mathrm{~km} / \mathrm{hr}$, the time taken by him to swim to a place $10 \mathrm{~km}$ upstream and back, is: (a) $8 \frac{1}{3} \mathrm{hr}$ (b) $9 \frac{1}{5} \mathrm{hr}$ (c) $10 \mathrm{hr}$ (d) $12 \mathrm{hr}$

A man can swim $3 \mathrm{~km} / \mathrm{hr}$ in still water. If the velocity of the stream be $2 \mathrm{~km} / \mathrm{hr}$, the time taken by him to swim to a place $10 \mathrm{~km}$ upstream and back, is:
(a) $8 \frac{1}{3} \mathrm{hr}$
(b) $9 \frac{1}{5} \mathrm{hr}$
(c) $10 \mathrm{hr}$
(d) $12 \mathrm{hr}$

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Key Concepts

Effective Speed Upstream and Downstream

In scenarios where an object moves against or with the flow of a medium, its speed changes accordingly. When moving upstream, the object’s effective speed is reduced by subtracting the medium’s speed from its still-water speed, while moving downstream, the effective speed is increased by adding the current velocity. This adjustment is crucial for accurately determining travel times in both directions.

Distance, Speed, and Time Relationship

This fundamental concept in kinematics states that the time taken for a journey is equal to the distance traveled divided by the speed of travel. When the speed is different for different segments of the journey, the time for each segment can be calculated separately and then added together to find the total time. This principle is widely used in solving problems related to motion.

Relative Velocity in Moving Mediums

This concept involves understanding that when an object, such as a swimmer, moves through a medium that itself is in motion (like a stream), the effective velocity relative to the ground is the vector sum of the object's velocity in still water and the velocity of the current. It lays the groundwork for solving problems where the motion is affected by an external factor like current speed.

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