Math 149. Capstone Mathematics for Teachers. Spring 2012.
Homework 4
Pooh, Pigglet, Tigger, and Eeyore ate a cake. They took turns, eating it just one person at a time. Each of them was eating exactly for the period of time that it
would take the other three to eat half of the cake. How much faster would they be done eating this cake if they were eating all at once instead of taking turns (assuming
they would eat at the same pace)?
Clarifications:
(1) They ate the whole cake.
(2) They could switch more than three times, but the total amount of time that each of them was eating was equal to the amount of
time that it would take the other three to eat half of the cake. So by rearranging their turns if necessary, we can assume that each of them ate their portion of the cake
in one sitting. E.g. first Pooh ate for the time that it would take Pigglet, Tigger, and Eeyore to eat half of the cake. Then Pigglet ate for the time that it would take
Pooh, Tigger, and Eeyore to eat half of the cake. Then it was Tigger's turn. Then Eeyore's turn. After Eeyore's turn, the whole cake was gone.
(3) The problem does not say that all four rates are equal. Only that each person always eats at the same rate, no matter whether they are alone at the table or
with their friends.
Find (or write your own) and solve 2 problems whose solutions may use proportional reasoning. Try to find one easy problem (that could be done in a typical Algebra I
or II class) and one hard/tricky problem (that could be discussed in a math club). For both problems, predict possible mistakes; show correct solutions using proportional
reasoning, and be sure to explain your reasoning. If a problem can be solved in different ways (whether or not they are using proportional reasoning), show as many
different solutions as you can find.