Word Problems

On Christmas Eve two candles, one of which was one inch longer than the other, were lighted.

The longer one was lighted at 4:30 p.m. and the shorter one at 6:00 p.m.

At 8:30 p.m. they were both the same length.

The longer one burned out at 10:30 p.m., and the shorter one at 10:00 p.m.

How long was each candle originally?

• Let the length of the shorter candle be x
• the length of the longer candle is x + 1 (because it is 1 inch longer)
• the short candle burns out in 4 hours
• the long candle burns out in 6 hours
• the length of the long candle:
  • x + 1 - T*(x + 1)/6 where T is the number of hours after 4:30
• the length of the short candle:
  • x - (1/4)*t*x where t is the number of hours after 6:00 at 8:30,
• they are both the same length.
  • T = 4,
• t = 1.5 x + 1 - 4*(x + 1)/6
  • =x - (1/4)*(3/2)*x x + 1 - (2/3)x - 2/3
  • = x - (3/8)x (1/3)x + 1/3
  • = (5/8)x
• multiply this by 24 8x + 8 = 15x 8 = 7x x = 8/7
• the short candle is 1 1/7 in.
• the long candle is 2 1/7 in.