Difference between revisions of "2002 AMC 8 Problems/Problem 6"
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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. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it? | 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. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it? | ||
| − | [[ | + | <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> | ||
Revision as of 10:50, 12 July 2021
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. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?
![[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 
.
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. 
