Difference between revisions of "1989 AHSME Problems/Problem 12"
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| + | == See also == | ||
| + | {{AHSME box|year=1989|num-b=11|num-a=13}} | ||
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| + | [[Category: Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 06:50, 22 October 2014
Problem
The traffic on a certain east-west highway moves at a constant speed of 60 miles per hour in both directions. An eastbound driver passes 20 west-bound vehicles in a five-minute interval. Assume vehicles in the westbound lane are equally spaced. Which of the following is closest to the number of westbound vehicles present in a 100-mile section of highway?
Solution
At the beginning of the five-minute interval, say the eastbound driver is at the point 
, and at the end of the interval at 
, having travelled five miles. Because both lanes are travelling at the same speed, the last westbound car to be passed by the eastbound driver was just west of the position 
at the start of the five minutes. The first westbound car to be passed was just east of at that time. Therefore, the eastbound driver passed all of the cars initially in the stretch of road between and . That makes 
cars in ten miles, so we estimate 
cars in a hundred miles.
![[asy] dot((0,0));dot((25,0));dot((50,0)); draw((15,5)--(5,5),EndArrow); draw((45,5)--(35,5),EndArrow); draw((0,0)--(50,0),dashed); draw((0,-5)--(10,-5),EndArrow); label("$0$",(0,0),W); label("$10$",(50,0),E); label("$5$",(25,0),S); [/asy]](http://latex.artofproblemsolving.com/6/f/6/6f6ffd2a5519bbefca300437631d23d33570a94c.png)
See also
| 1989 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
