Here is a graphical workbench that lets you explore a problem that many students have difficulty with:
Joe can paint a wall by himself in four hours.
Sam can paint the same wall by himself in two hours.
How long will it take them to paint the wall if they work together?
The graphical representation is in the walls/hr - hours plane
CHALLENGE –
a. Use this app to pose and solve a different problem
– Joe and Sam can each paint the wall alone in 3 hours.
b. Use this app to pose and solve a different problem
– Joe can paint the wall alone in 2 hours, and together Joe and Sam can paint the wall in one hour.
How long would it take Sam to paint the wall if he were painting by himself?
c. Make up a new problem like this in which Joe paints 3 times as fast as Sam.
d. Make up and solve a problem in which Joe, Sam and Mary all work on painting the wall.