Difference between revisions of "2004 AIME II Problems/Problem 5"
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Solution by rocketscience | Solution by rocketscience | ||
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| + | == See also == | ||
| + | {{AIME box|year=2004|num-b=4|num-a=6|n=II}} | ||
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| + | [[Category:Intermediate Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 18:58, 20 July 2017
Problem
In order to complete a large job, 
workers were hired, just enough to complete the job on schedule. All the workers stayed on the job while the first quarter of the work was done, so the first quarter of the work was completed on schedule. Then 
workers were laid off, so the second quarter of the work was completed behind schedule. Then an additional workers were laid off, so the third quarter of the work was completed still further behind schedule. Given that all workers work at the same rate, what is the minimum number of additional workers, beyond the 
workers still on the job at the end of the third quarter, that must be hired after three-quarters of the work has been completed so that the entire project can be completed on schedule or before?
Solution
A train is traveling at miles per hour and has one hour to reach its destination miles away. After 
minutes and 
miles it slows to 
mph, and thus takes 
minutes to travel the next miles. Then it slows to mph, so the next quarter takes 
. The train then has 
minutes left to travel 250 miles, and doing the arithmetic shows that during this last stretch it must travel more than 
mph to make it on time. Therefore the company needs to add 
more workers.
Solution by rocketscience
See also
| 2004 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
