Help with word problem?

Question

a girl noticed the expenive candles last only three hours each while the expensive candles last five hours each. the next evening, she hosted a party and lighted two candles- one from each box- at 7:30 pm. later, aguest noticed that ne candle was twice as log as th other. what time was this?

i'm thinking it happened in one hour but i could be wrong.

please explain why you got your answer

Answer 1

After x hours, the length of the cheaper candle as a fraction of it's total length is (3-x)/3.

Similarly the length of the more expensive one is (5-x)/5.

Assuming the two candles start the same length, then we need to find x when

2(3-x)/3 = (5-x)/5

=>30-10x = 15-3x

=>x=15/7.

Therefore one candle is twice as long as the other after 15/7 hours which is  2 hours 9 mins (to nearest minute).