Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

Two candles of equal length start burning at the same time. One of the candles will burn down in 4 hours and the other in 5 hours, each at their own constant rate.  How many hours will they have to burn before one candle is 3 times the length of the other?  Let the initial length of each candle be L. The faster candle burns at a rate of L over 4 and the slower at L over 5.  Since the slower candle is always longer than the faster one, we are looking for the time it takes for the slower one to be 3 times the length of the faster one.  After T hours, the slower candle has length L minus TL over 4 and the faster has length L minus TL over 5.  We solve for when the slower candle is 3 times the length of the faster candle.  Going through the algebra, we can find that this occurs at T equals 40 over 11 hours, which is our answer.

Video Summary

Two candles of equal length burn at different rates: one in 4 hours, the other in 5. We seek the time when the slower-burning candle is three times the length of the faster one. Given the initial length as L, the faster candle decreases by L/4 per hour and the slower by L/5 per hour. After T hours, the lengths become L-TL/4 and L-TL/5, respectively. Solving for when the slower candle is three times the faster candle's length, we find it occurs after 40/11 hours.

Keywords

candles

burning rates

length comparison

time calculation

mathematical solution