Difference between revisions of "2008 AMC 12A Problems/Problem 1"
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==Problem == | ==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? | + | A bakery owner turns on his doughnut machine at <math>\text{8:30}\ {\small\text{AM}}</math>. At <math>\text{11:10}\ {\small\text{AM}}</math> the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? |
− | <math>\ | + | <math>\mathrm{(A)}\ \text{1:50}\ {\small\text{PM}}\qquad\mathrm{(B)}\ \text{3:00}\ {\small\text{PM}}\qquad\mathrm{(C)}\ \text{3:30}\ {\small\text{PM}}\qquad\mathrm{(D)}\ \text{4:30}\ {\small\text{PM}}\qquad\mathrm{(E)}\ \text{5:50}\ {\small\text{PM}}</math> |
==Solution== | ==Solution== | ||
− | The machine completes one-third of the job in <math>\text{11:10}-\text{8:30}=\text{2:40}</math>. Thus the entire job is completed in <math>3 \cdot (\text{2:40}) = \text{8:00}</math>. Since the machine | + | The machine completes one-third of the job in <math>\text{11:10}-\text{8:30}=\text{2:40}</math> hours. Thus, the entire job is completed in <math>3\cdot(\text{2:40})=\text{8:00}</math> hours. |
+ | |||
+ | Since the machine was started at <math>\text{8:30 AM}</math>, the job will be finished <math>8</math> hours later, at <math>\text{4:30 PM}</math>. The answer is <math>\mathrm{(D)}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2008|ab=A|before=First question|num-a=2}} | {{AMC12 box|year=2008|ab=A|before=First question|num-a=2}} |
Revision as of 23:57, 25 April 2008
Problem
A bakery owner turns on his doughnut machine at . At the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
Solution
The machine completes one-third of the job in hours. Thus, the entire job is completed in hours.
Since the machine was started at , the job will be finished hours later, at . The answer is .
See Also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by First question |
Followed by Problem 2 |
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All AMC 12 Problems and Solutions |