Question

An office building loses a third of its heat between sundown and midnight and an additional half of the original amount of heat between midnight and 4 AM. If five-eighths of the remaining heat is lost between 4 AM and 5 AM, what proportion of the total heat loss occurs between 5 AM and sunrise?

Answer 1

Answer:

$\dfrac{1}{16}$

Step-by-step explanation:

Proportion of Heat Loss Between sundown and midnight$=\dfrac{1}{3}$

Proportion of Heat Loss between midnight and 4 AM  $=\dfrac{1}{2}$

Proportion of Total Heat Already Lost $=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}$

Proportion of Remaining Heat $=1-\dfrac{5}{6}=\dfrac{1}{6}$

Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.

Proportion of Heat Loss between 4 AM and 5 AM= $\dfrac{5}{8} X \dfrac{1}{6} = \dfrac{5}{48}$

Therefore, Proportion of Remaining Heat Left $=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}$

We therefore say that:

$\dfrac{1}{16} of the total heat loss occurs between 5 AM and sunrise.$