4
Part of 2007 AIME Problems
Problems(2)
Circular Orbits
Source: AIME I 2007 #4
3/15/2007
Three planets revolve about a star in coplanar circular orbits with the star at the center. All planets revolve in the same direction, each at a constant speed, and the periods of their orbits are 60, 84, and 140 years. The positions of the star and all three planets are currently collinear. They will next be collinear after years. Find .
LaTeXnumber theoryleast common multipleAMC
Whatsits and Whoosits
Source: AIME II 2007 #4
3/29/2007
The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, 100 workers can produce 300 widgets and 200 whoosits. In two hours, 60 workers can produce 240 widgets and 300 whoosits. In three hours, 50 workers can produce 150 widgets and m whoosits. Find m.
LaTeXAMCAIME II