Finding the Current of a Stream Pamela requires 3 hours to...

Name: Problem 70, Chapter 11: Precalculus
Uploaded: 2021-05-30T22:45:35-08:00
Duration: 1 min 45 s
Channel: Erika Bustos
Description: Finding the Current of a Stream Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela's average speed in still water. How fast is the current? (Assume that Pamela's speed is the same in each direction.)

Finding the Current of a Stream Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela's average speed in still water. How fast is the current? (Assume that Pamela's speed is the same in each direction.)

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Key Concepts

Relative Motion in a Current

This concept involves understanding that when an object moves in a flowing medium, its effective speed is altered by the speed of the medium. For movements downstream, the current adds to the object’s speed, while for upstream the current subtracts from it, making it a foundational idea in problems involving moving fluids like streams or rivers.

Speed, Distance, and Time Relationship

A core principle in motion problems is the relationship defined by the equation distance = speed × time. This relationship allows for the creation of equations that relate the speed of an object (and the speed of any medium currents) to the time taken to travel a given distance, providing a basis for solving for unknown variables.

Systems of Equations

When a problem provides multiple scenarios with different effective speeds, such as downstream and upstream travel, it typically leads to the formation of a system of equations. Solving these simultaneous equations by methods such as substitution or elimination enables the determination of individual quantities like the speed in still water and the current speed.

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