Difference between revisions of "2008 AMC 12A Problems/Problem 1"

Problem

A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?

$\textbf{(A)} \text{ 1:50 PM } \qquad \textbf{(B)} \text{ 3:00 PM } \qquad \textbf{(C)} \text{ 3:30 PM } \qquad \textbf{(D)} \text{ 4:30 PM } \qquad \textbf{(E)} \text{ 5:50 PM }$

Solution

The machine completes one-third of the job in $\text{11:10}-\text{8:30}=\text{2:40}$. Thus the entire job is completed in $3 \cdot (\text{2:40}) = \text{8:00}$. Since the machine is started at $\text{8:30 AM}$, the job is finished $8$ hours later at $\text{4:30 PM}\Rightarrow D$.