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Difference between revisions of "1989 AHSME Problems/Problem 12"
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label("$5$",(25,0),S);
 
label("$5$",(25,0),S);
 
</asy>
 
</asy>
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== See also ==
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{{AHSME box|year=1989|num-b=11|num-a=13}} 
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[[Category: Introductory Algebra Problems]]
 
{{MAA Notice}}
 
{{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?

$\textrm{(A)}\ 100\qquad\textrm{(B)}\ 120\qquad\textrm{(C)}\ 200\qquad\textrm{(D)}\ 240\qquad\textrm{(E)}\ 400$

Solution

At the beginning of the five-minute interval, say the eastbound driver is at the point $x=0$, and at the end of the interval at $x=5$, 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 $x=10$ at the start of the five minutes. The first westbound car to be passed was just east of $x=0$ at that time. Therefore, the eastbound driver passed all of the cars initially in the stretch of road between $x=0$ and $x=10$. That makes $20$ cars in ten miles, so we estimate $200$ 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]

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

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