Thread: Problem Solving

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.