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 ?

Question

anonymous · Answer

@ganeshie8

anonymous · Answer

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anonymous · Answer

i sure  the shrter one  is more fat :)

ganeshie8 · Answer

Haha is the answer 2 hours ?

anonymous · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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 $$5x-x*t \tag{1}$$

ganeshie8 · Answer

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 $$7x-2x*t \tag{2}$$

ganeshie8 · Answer

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

anonymous · Answer

ok got it... thanks for your help

ganeshie8 · Answer

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

dan815 · Answer

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