# 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:

$A=1/(1/15-1/(7.5/(1-13.5/15)))=\dfrac{ 75 }{ 4 }=18.8 \ \text{d}$
$\dfrac{1}{A}+\dfrac{1}{B} = \dfrac{1}{ 15 } \ \\ \ \\ r = 1 - 13.5/15 = 0.1 \ \\ r .... 7.5 \ \\ 1 .... B \ \\ \ \\ B = 7.5 / r = 75 \ \text{d} \ \\ \ \\ \dfrac{1}{A}+\dfrac{1}{B} = \dfrac{1}{ 15 } \ \\ \dfrac{1}{A} = \dfrac{1}{ 15 } - \dfrac{1}{B} \ \\ A = \dfrac{1}{ \dfrac{1}{ 15 } - \dfrac{1}{B}}= 18.75 \ \\$

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