Next up in the Shot Put competition, officials measured a throw to be 54 feet using 6 orange sticks exactly. How long are each of the sticks?

The opponent challenged the officials to measure with a purple stick that is 6 feet long. If the purple sticks were used to measure out the throw exactly, how many sticks must they have used?

Conveniently, both the purple and orange sticks measured the 54 foot throw exactly.

Are there any other shot put throw lengths where this would occur? Use a model to convince us.