Hello, Jimenez,

Candle heights, H, are 20cm and 24.5 cm for the two candles, given by H1 and H2. We know their rates of burn are 2.5 and 4 mm/hr. Let's put the units on the same bases so as not to get confused. 1 cm = 10mm, so I'll convert the heights to 200 and 245mm, respectively.

The height as a function of time will be the starting height minus the rate at which the candle burns multiplied by the time, in hours.

Candle 1: H1(t) = 200mm - (2.5mm/hr)*t, where t is time, in hours. At time = 0, we get the original height. After 2 hours, we lose 5mm of height, and so on.

Candle 2: H2(t) = 245mm - (4mm/hr)*t. This candle starts at 245 mm (t=0) and loses 4mm for each hour it burns.

To find how long each candle will last, set their heights to zero.

Candle1: 0 = 200mm -(2.5mm/hr)*t

t = 80 hours

Candle 2: Do the same thing and we find the life of the candle is 61.25 hours.

To determine the time their heights are equal, set each equation to equal to the other. In other words H1 = H2.

200 - 2.5t = 245 - 4t

t = 45/1.5, or 30 hours. Make the graph and you'll see where the lines cross, at 30 hours. Y should be the height in cm, and X is the time in hours.

You want to light the slowest candle first. It takes 80 hours. Since candle 2 takes 61.25 hours, take the difference (80 - 61.25 = 18.75 hours) and that will be the time to wait before starting the second candle.

I hope this helps,

Bob

Robert S.

11/23/20

JIMENEZ BONE M.

thank you so much !11/23/20