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
l1l2t1t2=3582=26=13

The intercept can be found from the point-slope formula by inserting one of the data points into the equation:
ll1=m(tt1)

With a little algebra we can show that
l=13t+173

And the length at time t=0 can be read off easily:
l=173=523

A quick sanity check... since 523 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 13 inch per minute?