Question

When the air codintener in a building is runnjng,tye temperature in the building changes at a rate of -1 °F every 18 minutes. At this rate,how many hours should it take to cool the building from a temperature of 85.5°F to a temperature of 78°F ? Round your answer ti the nearest hundredth

Answer 1

First let's calculate the difference in temperature:

$78-85.5=-7.5$

The change is -7.5°F. If the rate of change is -1°F every 18 minutes, we can use a rule of three to find the time needed for -7.5°F:

$\begin{gathered} -1\degree F\to18\text{ minutes} \\ -7.5\degree F\to x\text{ minutes} \\ \\ \frac{-1}{-7.5}=\frac{18}{x} \\ x=18\cdot7.5 \\ x=135 \end{gathered}$

So the time needed is 135 minutes. In hours, that is equal to:

$\frac{135}{60}=2.25$

So we have a time of 2.25 hours.