Hens & Rabbits - in {hen, rabbit} space

The two Hens & Rabbits applets represent the same problem in two different ways. A farmer has 50 animals. Some are hens and some are rabbits. Among them they have a total of 140 legs. How many hens and how many rabbits does the farmer have? [answer 30 hens, 20 rabbits] One graphical representation of the problem shows the problem in the {animals, feet} plane and the other graphical representation shows the problem in the {hens, rabbits} plane. Study the two representations carefully - How are the numbers of rabbits & the number of hens represented in the {animals, feet} plane? How are the number of animals and the number of feet represented in the {hens, rabbits} plane? How are the quantities feet/rabbit and feet/hen represented in each of the two planes? Which representation do you think provides you with more insight? Why?