The sum of the speeds of a boat in still water and the speed...

The sum of the speeds of a boat in still water and the speed the current is $10 \mathrm{kmph}$. If the boat takes $40 \%$ of the time to travel downstream when compared to that upstream, then find the difference of the speeds of the boat when travelling upstream and down stream. (1) $3 \mathrm{kmph}$ (2) $6 \mathrm{kmph}$ (3) $4 \mathrm{kmph}$ (4) $5 \mathrm{kmph}$

The sum of the speeds of a boat in still water and the speed the current is $10 \mathrm{kmph}$. If the boat takes $40 \%$ of the time to travel downstream when compared to that upstream, then find the difference of the speeds of the boat when travelling upstream and down stream.
(1) $3 \mathrm{kmph}$
(2) $6 \mathrm{kmph}$
(3) $4 \mathrm{kmph}$
(4) $5 \mathrm{kmph}$

Key Concepts

Boat Speed in Still Water

This concept refers to the speed at which a boat would travel if there were no external factors like currents. It is the inherent speed of the boat when computations of relative speeds are performed, and serves as a baseline in problems involving both upstream and downstream movement.

Current Speed

This is the speed of the water current in the river or stream. It affects the boat's effective speed, adding to it when moving downstream and subtracting from it when moving upstream, and is essential in determining the boat’s performance in different directions.

Relative Motion in Fluids

In problems involving boats traveling in streams, the effective speed of the boat is a result of its own speed in still water combined with the speed of the current. This concept of relative motion focuses on how combining speeds through addition or subtraction yields different effective speeds depending on the direction of travel.

Upstream and Downstream Speeds

This concept details how the effective speed of a boat is calculated differently based on the direction relative to the current. When going downstream, the boat's speed increases due to the current, while upstream, it is reduced by the current. This concept is crucial for establishing relationships between time, distance, and speed in riverine contexts.

Time-Speed Relationship

This principle states that when traveling a fixed distance, the time taken is inversely proportional to the speed of travel. In the context of river problems, comparing the time taken upstream versus downstream helps in formulating equations that relate the boat's speed in still water and the speed of the current.

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