I need help with this Algebra Question.

Question

Mrs. Bruton recently purchased two boxes of ten-inch candles; one box from a discount store, the other from an expensive boutique. It so happens that the inexpensive candles last only three hours each, while the expensive candles last five hours each. One evening, Mrs. B. hosted a dinner party and lit two of the candles (one from each box) at 7:30 pm. During dessert, a guest noticed that one candle was twice as long as the other. At what time was this observation made?

Answer 1

The equation for the length of the good candle is L_g = -2t + 10

The equation for the length of the bad candle is L_b = -(10/3) + 10

The length of the good candle is twice the length of the bad candle when -2t + 10 = 2 { -(10/3)t + 10 }

Solving for t, we find that t = 15/7 hours or about 2 hours 8.6 minutes

So the time would of the observation would be 7:30pm + 2 hours & 8.6 minutes or about 9:39pm