Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 14 days, B together with C for 23 days, A together with C for 13 days.

How long it would take to complete the task every one of them alone?
How long it would take to complete the task, if all three work together?

Correct result:

A =  19.07 d
B =  52.65 d
C =  40.84 d
x =  10.4259 d

Solution:

$$\begin{gathered} {\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{B}}={\displaystyle \frac{1}{14}} \\ {\displaystyle \frac{1}{B}}+{\displaystyle \frac{1}{C}}={\displaystyle \frac{1}{23}} \\ {\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{C}}={\displaystyle \frac{1}{13}} \\ a=19.07\text{ d} \end{gathered}$$

$b=52.65\text{ d}$

$c=40.84\text{ d}$

$$\begin{gathered} {\displaystyle \frac{1}{t}}={\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{B}}+{\displaystyle \frac{1}{C}} \\ t={\displaystyle \frac{1}{{\displaystyle \frac{1}{A}}+{\displaystyle \frac{1}{B}}+{\displaystyle \frac{1}{C}}}} \\ t=10.4259\text{ d} \end{gathered}$$

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