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

`(1)/(16)`

Explanation:

Proportion of Heat Loss Between sundown and midnight
`=(1)/(3)`

Proportion of Heat Loss between midnight and 4 AM
`=(1)/(2)`

Proportion of Total Heat Already Lost
`=(1)/(3)+(1)/(2) =(5)/(6)`

Proportion of Remaining Heat
`=1-(5)/(6)=(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=
`(5)/(8)$ X (1)/(6) = (5)/(48)`

Therefore, Proportion of Remaining Heat Left
`=(1)/(6)- (5)/(48)=(1)/(16)`

We therefore say that:

`(1)/(16)$ of the total heat loss occurs between 5 AM and sunrise.`