Difference between revisions of "2022 AMC 8 Problems/Problem 9"
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After <math>15</math> minutes, the difference between the temperatures is <math>36\div2=18</math> degrees Fahrenheit. At this point, the water temperature is <math>68+18=\boxed{\textbf{(B) } 86}</math> degrees Fahrenheit. | After <math>15</math> minutes, the difference between the temperatures is <math>36\div2=18</math> degrees Fahrenheit. At this point, the water temperature is <math>68+18=\boxed{\textbf{(B) } 86}</math> degrees Fahrenheit. | ||
− | ~MRENTHUSIASM | + | <u><b>Remark</b></u> |
+ | |||
+ | Alternatively, we can condense the solution above into the following equation: <cmath>68+(212-68)\cdot\left(\frac12\right)^{15/5}=86.</cmath> | ||
+ | ~MRENTHUSIASM ~Mathfun1000 | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=8|num-a=10}} | {{AMC8 box|year=2022|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 22:25, 28 January 2022
Problem
A cup of boiling water () is placed to cool in a room whose temperature remains constant at
. Suppose the difference between the water temperature and the room temperature is halved every
minutes. What is the water temperature, in degrees Fahrenheit, after
minutes?
Solution
Initially, the difference between the water temperature and the room temperature is degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit. At this point, the water temperature is
degrees Fahrenheit.
Remark
Alternatively, we can condense the solution above into the following equation:
~MRENTHUSIASM ~Mathfun1000
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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.