What was the original length of the candle if a candle is burning at a linear rate and the candle measures five inches two minutes after it was lit and it measures three inches eight minutes after it was lit?

1 Answer
Dec 18, 2014

This is a problem where you are given two positions on a graph and are asked to find the equation of the line connecting them. In this case you are also being asked for the #y# intercept of the graph.

The independent variable is time. We'll plot that on the x-axis. The dependent variable is the length of the candle. That will be the y-axis.

At two minutes the length of the candle is 5 inches.
#t = 2, l=5#
At eight minutes the length of the candle is 3 inches.
#t = 8, l=3#

We need to find the equation of a line which goes through the two points #(2,5) and (8,3)#.

The slope is easy to find
#(l_1-l_2)/(t_1-t_2) = (3-5)/(8-2) = -2/6 = -1/3#

The intercept can be found from the point-slope formula by inserting one of the data points into the equation:
#l-l_1 = m(t-t_1)#

With a little algebra we can show that
#l = -1/3 t + 17/3#

And the length at time #t=0# can be read off easily:
#l = 17/3 = 5 2/3#

A quick sanity check... since #5 2/3# is larger than 5 (the length at 2 minutes) the answer makes sense.

What sort of candle do you think would burn at a rate of #1/3# inch per minute?