A fishing boat travels along the east coast of the United...

A fishing boat travels along the east coast of the United States and encounters the Gulf Stream current. It travels $44 \mathrm{mi}$ north with the current in $2 \mathrm{hr}$. It travels $56 \mathrm{mi}$ south against the current in $4 \mathrm{hr}$. Find the speed of the current and the speed of the boat in still water.

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Key Concepts

Uniform Motion Principle

This principle states that distance equals speed multiplied by time. It is a fundamental concept used to relate the three variables in any motion problem, forming the basis for setting up equations that describe how far an object travels over a given period.

Relative Velocity

Relative velocity refers to the effective speed of an object when additional factors such as currents or winds are involved. In such cases, the object's speed is either increased or decreased depending on whether it is moving with or against the external medium.

Speed in Still Water vs. Current Speed

This concept distinguishes between the intrinsic speed of the boat (its speed in still water) and the speed of the current that influences its actual travel speed. When the boat moves in the same direction as the current, you add the current’s speed to the boat’s speed; when it moves against, you subtract the current’s speed from the boat’s speed.

Systems of Linear Equations

In problems involving multiple scenarios that yield different equations, a system of linear equations is used to represent the relationships among the unknown variables. By solving this system, one can determine individual values such as the boat’s speed in still water and the speed of the current.

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