Thread: Problem Solving

There are two candles, a short one, and a long one. Each candle has different widths, and lengths, but burns at the same rate. The short candle can burn for 20 hours, while the long candle can burn for 14 hours. After 5 hours of burning, the length of the long candle is the same as the length of the short candle. What is the original ratio s of lengths of the candles?

The question is asking for the ratio, s, of the original lengths of the two candles.

Let x = initial length of the short candle
And y = initial length of the long candle

Their rates of burning:
Length = rate time
Or,
rate = length / time

For x, since it will burn for 20 hrs,
rate = x/20 (units of length)/hr
After 5 hrs burning, what is left is
x -(x/20)(5)
= x -x/4
= 3x/4 units of length

For y, that will burn out after 14 hrs,
rate = y/14 (units of length)/hr
After 5 hours burning, what is left is
y - (y/14)(5)
= (14y -5y)/14
= 9y/14 units of length

Those two leftovers are equal in length, so,
3x/4 = 9y/14
Cross multiply,
42x = 36y ------(i)

we are looking for ratio s ......which can be x/y or y/x.
Say we get s = x/y
Divide both sides of (i) by y,
42x/y = 36
x/y = 36/42 = 6/7

Therefore, s = x/y = 6/7 --------------answer.