A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.

We have twelve inch candle and an 18 inch candle are lit at 6pm and the 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns 2 inch every hour.

Height 18 inch candle after h hours, = 18 - 2h

Height 12 inch candle after h hours, = 12 - 0.5h

At same height we have

18 - 2h = 12 - 0.5h

1.5 h = 18 - 12

h = 4 hours.

Time = 6 PM + 4 hours = 10 PM

At 10 PM both candles will be same height.

aksnkj aksnkj · Answer 2 · 2021-10-03T16:29:05+02:00

Answer:

At 10 PM, both the candles will be of same height.

Step-by-step explanation:

Two candles are lit at 6 PM.

The length of candles is 12 inch and 18 inch.

The rate of burning of 12 inch candle is 0.5 inch per hour.

The rate of burning of 18 inch candle is 2 inch per hour.

Let [tex]h[/tex] represents the number of hours of burning.

In [tex]h[/tex] hours, the remaining length of the 12 inch candle will be,

[tex]l_1=12-0.5\times h[/tex]

In [tex]h[/tex] hours, the remaining length of the 18 inch candle will be,

[tex]l_2=18-2\times h[/tex]

Now, it is required to find the time at which the length of both the candles will be same.

So, the time [tex]h[/tex] in hours will be,

[tex]l_1=l_2\\12-0.5h=18-2h\\1.5h=6\\h=4\rm hour[/tex]

So, after 4 hours, both the candles will be of same length.

Therefore, the time will be [tex]6+4=10[/tex] PM. At 10 PM, both the candles will be of same height.

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https://brainly.com/question/14070528?referrer=searchResults