Boiler room

If only the first boiler is running, the coal supply lasts 8 days. If only the second boiler is running, the supply lasts 12 days. If only the third boiler is running, the supply lasts 6 days.
How many days in total will the coal supply last if only the first boiler runs for the first two days, after which the other two boilers are also switched on?

Final 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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