from Polya - Mathematical Discovery
A man walked 5 hrs, first along a level road, then up a hill, then he
turned around walked back to his starting point along the same route.
He walks 4 mi/hr on the level, 3 mi/hr uphill and 6 mi/hr downhill.
What was the total distance that he walked?
Solve this problem algebraically and use this environment
to solve it graphically. [you can set times by dragging the large
dots.]
Show that the solution depends on the particular choice of numbers -
In general the problem is indeterminate.
What has to be true about the relationship among the three speeds
for the problem to be soluble?
[You can explore an ensemble of similar problems by varying the speeds.
Check the 'your own' box in the left panel.]