Homework 11

Make sure you completely justified all your answers.

1. (MH 9-10, 2009) 5 cows can eat 2 acres of grass in 10 days. How many days will it take 10 cows to eat 6 acres of grass?

2. (MH 9-10, 2009) Two telephone poles x and y feet tall are placed M feet apart. Lines are drawn from the top of each pole to the bottom of the other pole. How many feet along the ground from the pole that is x feet high will the lines from the two poles intersect?

3. 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.