Question

One candle is 50cm high and can burn for 3 hours. Another one is 70cm high and can burn for 6 hours. How long does it take for this two candles to reach the same height?​

Answer 1

One candle is 50cm50cm high and can burn for 3hr3hr another one is 70cm70cm high and can burn for 6hr6hr

Speed of burning of first candle =\frac{50}{3}=

3

50

cm/hr

Speed of burning of second candle=\frac{70}{6}= \frac{35}{3}=

6

70

=

3

35

cm/hr

Let the new lengths after burning of first second candle be x\,cmxcm

Let the time taken to burn be t\,hrthr

Distance traveled by the first candle will be (50-x)cm(50−x)cm

And distance traveled by the second candle will be (70-x)cm(70−x)cm

Now,

Distance = speed × time

∴ (50-x)=\frac{50}{3}\times t(50−x)=

3

50

×t __1

And (70-x)=\frac{35}{3}\times t(70−x)=

3

35

×t __2

Substituting equation-2 & 1,

∴(70-x-50+x)=\frac{35t}{3}-\frac{50t}{3}(70−x−50+x)=

3

35t

−

3

50t

⇒20\times 3=-15t20×3=−15t

∴t=-4\,hrt=−4hr

∴ Time take for this two candles to reach the same height is 4\, hr4hr