2022 AMC 8 Problems/Problem 9

Problem

A cup of boiling water ( $212^{\circ}\text{F}$ ) is placed to cool in a room whose temperature remains constant at $68^{\circ}\text{F}$ . Suppose the difference between the water temperature and the room temperature is halved every $5$ minutes. What is the water temperature, in degrees Fahrenheit, after $15$ minutes?

$\textbf{(A) } 77 \qquad \textbf{(B) } 86 \qquad \textbf{(C) } 92 \qquad \textbf{(D) } 98 \qquad \textbf{(E) } 104$

Solution 1

Initially, the difference between the water temperature and the room temperature is $212-68=144^{\circ}\text{F}$ . After $15$ minutes, the difference would be decreased by a factor of $2^{\tfrac{15}{3}}=8$ . Now, the difference is $144\div8=18^{\circ}\text{F}$ . Finally, the water temperature is $68+18=\boxed{\textbf{(B) } 86}$ degrees Fahrenheit.

~MRENTHUSIASM

~MathFun1000 (Conciseness)

2022 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All AJHSME/AMC 8 Problems and Solutions

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2022 AMC 8 Problems/Problem 9

Problem

Solution 1

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