Question
Tue September 01, 2009 By: M-vidya Sagar

It is on simultaneous linear equation

Expert Reply
Wed September 02, 2009

Let the length of the shorter candle be x.cm

Then, the length of the longer candle = (x + 3) cm

The shorter candle burn out in 9/2  hours.

So, the rate of burning of shorter candle = 2x /9

Similarly the longer candle burns out in 11/2 hours.

So, the rate of burning of longer candle = 2(x+3) / 11

Let us compute the length of the shorter candle after 5/2 hours which is

Length of candle burnt after 5/2 hours = 2x/9 x (5/2)

                                                                     = 5x/9

Actual length of shorter candle after 5/2 hours = x - 5x/9 = 4x/9 .....................(1)

Now, let us compute the length of the longer candle after 4 hours which is

Length of candle burnt after 5/2 hours = 2(x+3)/11 x 4

                                                                     = 8(x+3)/11

Actual length of longer candle after 4 hours = (x+3) - (8(x+3)/11)

                                                                              = (3(x+3))/11 .................................(2)

Now according to the question, the length of the two candles at 9:30 are equal.

Therefore, 4x/ 9 = 3x + 9/ 11

⇒ 44x = 27x + 81

⇒ 14 x = 81

So, x = 5.78 cm

 

                                                              

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