Question

1. the temperature of a cup of coffee changed by - 54°f over 22\frac{1}{2} minutes. what was the change in temperature each minute?

Explanation:

Step1: Convert mixed - number to improper fraction

$22\frac{1}{2}=\frac{22\times2 + 1}{2}=\frac{45}{2}$

Step2: Calculate the rate of temperature change

We want to find the change in temperature per minute. We divide the total change in temperature by the total number of minutes. Let $r$ be the rate of change of temperature per minute. Then $r=\frac{- 54}{\frac{45}{2}}$. Using the rule of dividing by a fraction ($a\div\frac{b}{c}=a\times\frac{c}{b}$), we have $r=-54\times\frac{2}{45}$.

Step3: Simplify the fraction

$-54\times\frac{2}{45}=\frac{-54\times2}{45}=\frac{-108}{45}$. Simplify $\frac{-108}{45}$ by dividing both the numerator and denominator by 9. We get $\frac{-12}{5}=-2.4$.

Answer:

$-2.4^{\circ}F$