Question

A candle is lit and the length of the burning candle changes at a constant rate of -1.6 inches per hour. 3 hours after the candle was lit the candle was 8.7 inches long. Determine how long the candle was before it was lit.

Answer 1

Answer: The length of the candle was 13.5 inches before it was lit.

Step-by-step explanation:

Let the length of candle in the beginning be c.

Constant rate of change in length of candle=  -1.6 inches per hour

Since rate of change is constant so the length of candle can be represented by a linear function [Linear function has constant rate of change.]

Linear function : f(x)= mx+c , where x= independent variable.

m= constant rate of change and c= initial value of function.

Let x = Number of hours after the candle was lit.

Put m=  -1.6 , x= 3 and f(x)= 8.7 , we get

$8.7=-1.6(3)+c\\\\ 8.7= -4.8+c\\\\ c=8.7+4.8=13.5$

Hence, the length of the candle was 13.5 inches before it was lit.