Sparklers

Roman lit his 10 equally-sized sparklers one by one on New Year's Eve. He lit the first one. When only one tenth of it remained, he lit the second one; when only one tenth of that remained, he lit the third, and so on. The sparklers burn at a constant rate along their entire length. One sparkler burns completely in 2 minutes.
How long did it take for all 10 sparklers to burn out?

Final Answer:

t =  1092 s
m =  18 min
s =  12 s

Step-by-step explanation:

$$\begin{gathered} t_0=2\cdot 60=120\text{s} \\ {t}_1=t_0\cdot (1-1/10)=120\cdot (1-1/10)=108\text{s} \\ t=10\cdot t_1+(t_0-t_1)=10\cdot 108+(120-108)=1092\text{s} \end{gathered}$$

$m=\lfloor t/60\rfloor =\lfloor 1092/60\rfloor =18\text{min}$

$s=t-60\cdot m=1092-60\cdot 18=12\text{s}$

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