2024 AMC 10A Problem 8

Amy, Bomani, Charlie, and Daria work in a chocolate factory. On Monday Amy, Bomani, and Charlie started working at

1{:}00\text{ 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

2{:}45\text{ PM}

. At what time did Daria join the group?

\text{(A)}\;\text{1:25 PM}

\text{(B)}\;\text{1:35 PM}

\text{(C)}\;\text{1:45 PM}

\text{(D)}\;\text{1:55 PM}

\text{(E)}\;\text{2:05 PM}