## anonymous one year ago Robert bought 2 different candles. the ratio of short candle to the longer candle is 5 : 7. it is known that the longer candle when lighted can melt in 3.5 hours while the shorter candle when lighted can melt in 5 hours. now the two candles are lighted at the same time. after how many hours will the length of two candles be exactly equal ?

1. anonymous

@ganeshie8

2. anonymous

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3. anonymous

i sure the shrter one is more fat :)

4. ganeshie8

Haha is the answer 2 hours ?

5. anonymous

im asking this problem, so i dont know the answer. can you show how to get that ?

6. ganeshie8

Easy... Let $$5x$$ = length of the short candle in meters $$7x$$ = length of the longer candle in meters $$t$$ = time elapsed in hours after the candles are lit

7. ganeshie8

rate of melting of short candle = $$\large \frac{5x ~\text{meters}}{5 \text{hours}} = x\text{ meters/hour}$$ starting length of short candle = $$5x$$ The length short candle after $$t$$ hours is given by $5x-x*t \tag{1}$

8. ganeshie8

rate of melting of long candle = $$\large \frac{7x ~\text{meters}}{3.5 \text{hours}} = 2x\text{ meters/hour}$$ starting length of short candle = $$7x$$ The length longer candle after $$t$$ hours is given by $7x-2x*t \tag{2}$

9. ganeshie8

set both equation equal to each other and solve $$t$$

10. anonymous

ok got it... thanks for your help

11. ganeshie8

weird, the time at which the candles get to same heights doesn't depend on their starting lengths

12. dan815

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13. dan815

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14. dan815

i dont know why i even change the ratio lol

15. dan815

heres a ssimple way

16. dan815

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17. dan815

which is nice to look at, that the candle is burning exactly 2 times faster