Two candles have different lengths and thickness. The longer one can burn for 6 hours and the shorter one for 9 hours. After 3 hours of burning, both candles have the same length. The shorter candle's length divided by the longer candle's length was?
let the shorter have an original length of x units
let the longer have an original length of y units
rate of the shorter = x/6
rate of the longer = y/9
length of shorter after 3 hours = x - 3x/6 = x - x/2 = x/2
lenght of longer after 3 hours = y - 3y/9 = y - y/3 = 2y/3
but x/2 = 2y/3
3x = 4y
x/y = 4/3
oops
Please reverse my definitions,
the shorter is y
the longer is x
so longer/shorter = 4/3
Thanks Rainy
Sorry *Reiny*
Why is it x - 3x/9, why is it 3 times x?
Please reply Reiny
Reiny, I'm still a bit confused. I have the same question that Shubham has. Could you please explain a bit more clearly?
Sandavi/Shubham -- how can we take you seriously? You are apparently the same person who is talking to yourself.
To solve this problem, we can use a mathematical approach. Let's assume the length of the longer candle is L and the length of the shorter candle is S.
We are given that the longer candle can burn for 6 hours and the shorter candle can burn for 9 hours. After 3 hours of burning, both candles have the same length.
Let's calculate the rate at which each candle burns. The rate at which a candle burns is given by the length of the candle divided by the time it can burn.
For the longer candle:
Rate of burning = L / 6 hours
For the shorter candle:
Rate of burning = S / 9 hours
After 3 hours of burning, both candles have the same length. This means that the amount of candle burned for both candles is the same.
For the longer candle:
Amount of candle burned = Rate of burning × Time = (L / 6) × 3 = L/2
For the shorter candle:
Amount of candle burned = Rate of burning × Time = (S / 9) × 3 = S/3
Since the amount of candle burned for both candles is the same, we can set up an equation:
L/2 = S/3
To find the ratio between the lengths of the candles, we can rearrange the equation:
S/L = 3/2
Therefore, the shorter candle's length divided by the longer candle's length is 3/2 or 1.5.