Workers

Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days.

If every worker was working alone, how many days took whole work for worker A and B?

Correct result:

A =  18.8 d
B =  75 d

Solution:

$A=1\mathrm{/}(1\mathrm{/}15-1\mathrm{/}(7.5\mathrm{/}(1-13.5\mathrm{/}15)))={\displaystyle \frac{75}{4}}\text{ d}=18.8\text{ d}$

$$\begin{gathered} {\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{B}}={\displaystyle \frac{1}{15}} \\ r=1-13.5\mathrm{/}15=0.1 \\ r\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}7.5 \\ \mathrm{1....}B \\ B=7.5\mathrm{/}r=75\text{ d } \\ {\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{B}}={\displaystyle \frac{1}{15}} \\ {\displaystyle \frac{1}{A}}={\displaystyle \frac{1}{15}}-{\displaystyle \frac{1}{B}} \\ A={\displaystyle \frac{1}{{\displaystyle \frac{1}{15}}-{\displaystyle \frac{1}{B}}}}=18.75 \end{gathered}$$

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