Difference between revisions of "2002 AMC 8 Problems/Problem 6"
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| − | ==Problem | + | ==Problem== |
| − | A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. | + | A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. Which one of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time? |
| + | <asy> | ||
| + | size(450); | ||
| + | defaultpen(linewidth(0.8)); | ||
| + | path[] p={origin--(8,8)--(14,8), (0,10)--(4,10)--(14,0), origin--(14,14), (0,14)--(14,14), origin--(7,7)--(14,0)}; | ||
| + | int i; | ||
| + | for(i=0; i<5; i=i+1) { | ||
| + | draw(shift(21i,0)*((0,16)--origin--(14,0))); | ||
| + | draw(shift(21i,0)*(p[i])); | ||
| + | label("Time", (7+21i,0), S); | ||
| + | label(rotate(90)*"Volume", (21i,8), W); | ||
| + | } | ||
| − | + | label("$A$", (0*21 + 7,-5), S); | |
| + | label("$B$", (1*21 + 7,-5), S); | ||
| + | label("$C$", (2*21 + 7,-5), S); | ||
| + | label("$D$", (3*21 + 7,-5), S); | ||
| + | label("$E$", (4*21 + 7,-5), S); | ||
| + | </asy> | ||
<math>\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}</math> | <math>\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}</math> | ||
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==Solution== | ==Solution== | ||
The change in the water volume has a net gain of <math>20-18=2</math> millimeters per minute. The birdbath's volume increases at a constant rate until it reaches its maximum and starts overflowing to keep a constant volume. This is best represented by graph <math>\boxed{\text{(A)}\ A}</math>. | The change in the water volume has a net gain of <math>20-18=2</math> millimeters per minute. The birdbath's volume increases at a constant rate until it reaches its maximum and starts overflowing to keep a constant volume. This is best represented by graph <math>\boxed{\text{(A)}\ A}</math>. | ||
| + | |||
| + | ==Video Solution by WhyMath== | ||
| + | https://youtu.be/00QQlJHSGxc | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2002|num-b=5|num-a=7}} | {{AMC8 box|year=2002|num-b=5|num-a=7}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 13:28, 29 October 2024
Problem
A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. Which one of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time?
![[asy] size(450); defaultpen(linewidth(0.8)); path[] p={origin--(8,8)--(14,8), (0,10)--(4,10)--(14,0), origin--(14,14), (0,14)--(14,14), origin--(7,7)--(14,0)}; int i; for(i=0; i<5; i=i+1) { draw(shift(21i,0)*((0,16)--origin--(14,0))); draw(shift(21i,0)*(p[i])); label("Time", (7+21i,0), S); label(rotate(90)*"Volume", (21i,8), W); } label("$A$", (0*21 + 7,-5), S); label("$B$", (1*21 + 7,-5), S); label("$C$", (2*21 + 7,-5), S); label("$D$", (3*21 + 7,-5), S); label("$E$", (4*21 + 7,-5), S); [/asy]](http://latex.artofproblemsolving.com/c/9/0/c90f5a436d6ce351c15b3ce838df936ff3ea4a35.png)
Solution
The change in the water volume has a net gain of 
millimeters per minute. The birdbath's volume increases at a constant rate until it reaches its maximum and starts overflowing to keep a constant volume. This is best represented by graph 
.
Video Solution by WhyMath
See Also
| 2002 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
