This applet is a graphical workbench that lets you explore a problem that many students have difficulty with:[br][br][i][b]Joe can paint a wall by himself in four hours.[br]Sam can paint the same wall by himself in two hours[br]How long will it take them to paint the wall if they work together?[/b][br][/i][br]The representation is in the walls, time plane.[br][br]Assuming the start at the same time, the app shows the fraction of the wall [br]painted at any time by Joe and by Sam. It can also show the fraction of the wall [br]painted at any time by the two of them painting together.[br][br]You can use the app to find the answer to the question very simply. [br][br]Now, write an equation relating the rates at which Joe and Sam can each paint the wall and [br]the length of time it takes them to do so together.[br][br]CHALLENGE – [br][br]a. How is the GREEN function related to the RED and BLUE functions?[br]b. Use this app to solve a different problem – Joe and Sam can each paint the wall alone in 3 hours.[br]c. Use this app to solve a different problem – [br] Joe can paint the wall alone in 2 hours, and together Joe and Sam can paint the wall in one hour. [br] How long would it take Sam to paint the wall if he were painting by himself?[br]d. Make up a new problem like this in which Joe paints 3 times as fast as Sam.[br]e. Make up and solve a problem in which Joe, Sam and Mary all work on painting the wall.

[color=#1551b5][i] [b] - GOING FURTHER[br][br]How does this applet compare to "Combining rates - II - upstream, downstream"?[br][br]How is it similar? different?[/b][/i][/color]