Question

A ten-inch candle is being burned at both ends. one end burns at the rate of one inch per hour; the other end, one-and-a-half inches per hour. how far from the center of the candle will the burning ends meet?

Answer 1

First keep in mind that the center is 5 inches...let L and R be the left and right positions of the two flames...

L=h and R=10-1.5h  where h is in hours....

The two flames meet when L=R so we can say:

h=10-1.5h  add 1.5h to both sides

2.5h=10  divide both sides by 2.5

h=4

So the flames will meet in five hours, using either original equation we can find this position, I'll use L=h..

L=4

So the position of the flames is 4" from the end.  The questions ask how far this point is from the center so:

5-4=1"

So the flames meet 1 inch from the center.