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Typical Problems for River Current
1. Level 1 - Well Stated
A boat travels downstream on a river at 60 km/h. It travels upstream on the same river at 40 km/h. What is the speed of the boat in still water and the speed of the current of the river? Assume that the speed of the boat in still water and speed of the current of the river are constant.
2. Level 1 - Poorly Stated
A boat travels downstream at 60 km/h and upstream at 40 km/h. With what speed would a raft move?
3. Level 2 - Well Stated
A boat went 15km downstream in 20 minutes and then upstream 50km in 2 hours. At what speed would a piece of driftwood move in this river? Assume that the speed of the boat in still water and speed of the current of the river are constant.

InterActivity     

Click and drag the sliders to set: speed of boat in still water, speed of current and direction of boat.

Then click on the animation buttons:   
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Problem Solving Techniques

 

\left\{ \matrix{ \color{red}{x + y = 60} \cr \color{blue}{x - y = 40} \cr} \right. \Leftrightarrow \left\{ \matrix{ x + y = 60 \cr \color{purple}{2x + 0y = 100} \cr} \right. \Leftrightarrow \left\{ \matrix{ x + y = 60 \cr \color{purple}{2x = 100} \cr} \right.

 

 

Mathcasts

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Comments on this type of problem

Positive

  • The "weight" of the problem is in the setup of the equation/equations.
  • Once setup - the solution is straightforward.
  • It is a fairly realistic problem.

Negative

  • Usually this type of problem is so badly stated - if a student hasn't solved one like it in class, he won't even understand what is being asked!
  • It is more natural to setup with two equations in two unknowns, but frequently a student is required to solve it using only one unknown.
Metadata
Global Wind and River Current Problem Solving
Brief Examines the idea of wind and river current adding and subtracting from the speed of plane or boat.
Grade 8    (good problem for beginning systems of equations 2x2)
Strand Algebra 1 AF at Math247

Matrix Algebra Algebra at Math247

Standard Algebra 1 3.4 ACT EE 28-32
Keywords linear, equation, system, 2 variables, algebra, dynamic, freeware, applet, offline, online
Comments Images are terrible - looking for new ones :)
Download coming soon
Author LFS - contact
Type Freeware - Available for Offline and Online Use - Translatable (html)
Use Requires sunJava player

 


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Page last modified on March 15, 2009, at 04:48 AM