Boiler room

If only the first boiler is running, the coal supply is enough for 8 days. If only the second boiler is running, the coal supply is enough for 12 days. If only the third boiler is in operation, the coal supply will last for 6 days.
How many days in total will the coal supply last if only the first boiler is in operation for the first two days and then the two remaining boilers are also switched on?

Correct answer:

x =  5

Step-by-step explanation:

$$\begin{gathered} t_1=2\text{d} \\ {k}_1=\frac{1}{8}=0.125 \\ {k}_2=\frac{1}{12}\doteq 0.0833 \\ {k}_3=\frac{1}{6}\doteq 0.1667 \\ {k}_{23}=k_2+k_3=\frac{1}{12}+\frac{1}{6}=\frac{1}{12}+\frac{2}{12}=\frac{1+2}{12}=\frac{3}{12}=\frac{1}{4}=0.25 \\ {t}_1\cdot k_1+(x-t_1)\cdot k_{23}=1 \\ 2\cdot 0.125+(x-2)\cdot 0.25=1 \\ 0.25x=1.25 \\ x=\frac{1.25}{0.25}=5 \\ x=5 \end{gathered}$$

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