Painters 4

One painter can do a job in 12 days. After 4 1/3 days, a second painter comes to help, and together they complete the work in 8 days. How long would the second painter take to do the job alone?

Final Answer:

x =  11 d

Step-by-step explanation:

$$\begin{gathered} a=4\frac{1}{3}=4+\frac{1}{3}=\frac{4\cdot 3+1}{3}=\frac{12+1}{3}=\frac{13}{3}\doteq 4.3333 \\ s=8 \\ b=8-a=8-\frac{13}{3}=\frac{8\cdot 3}{3}-\frac{13}{3}=\frac{24}{3}-\frac{13}{3}=\frac{24-13}{3}=\frac{11}{3}\doteq 3.6667 \\ s/12+b/x=1 \\ x\cdot \frac{s}{12}+b=x \\ x\cdot \frac{8}{12}+3.6666666666667=x \\ x\cdot 8/12+3.6666666666667=x \\ 4x=44 \\ x=\frac{44}{4}=11 \\ x=11=11\text{d} \end{gathered}$$

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