Problem:
Amy, Bomani, Charlie, and Daria work in a chocolate factory. On Monday Amy, Bomani, and Charlie started working at 1:00 PM and were able to pack 4, 3, and 3 packages, respectively, every 3 minutes. At some later time, Daria joined the group, and Daria was able to pack 5 packages every 4 minutes. Together, they finished packing 450 packages at exactly . At what time did Daria join the group?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Every 3 minutes, Amy, Bomani, and Charlie together packed 10 packages. From 1:00 PM to , a span of minutes, these three packers packed packages. This means that Daria must have packed packages. The time needed for Daria to pack 100 packages is minutes. Therefore Daria joined the group at , which is 80 minutes before .
The problems on this page are the property of the MAA's American Mathematics Competitions