Problem:
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, workers can produce widgets and whoosits. In two hours, workers can produce widgets and whoosits. In three hours, workers can produce widgets and whoosits. Find .
Solution:
The fact that workers produce widgets and whoosits in two hours implies that workers produce widgets and whoosits in two hours, or widgets and whoosits in one hour. Let be the time required for a worker to produce a widget, and let be the time required for a worker to produce a whoosit. Then , which is equivalent to . In three hours, workers produce widgets and whoosits, so and . Solving the last equation yields .
The problems on this page are the property of the MAA's American Mathematics Competitions