# Two workers

One worker needs 40 hours to do a job, and the second would do it in 30 hours. They worked together for several hours, then the second was recalled, and the first completed the job itself in 5 hours. How many hours did they work together, and how much did each of them do?

Result

x =  15 h
a =  0.5
b =  0.5

#### Solution:

$\ \\ x \cdot \ (1/40+1/30) + 5/40 = 1 \ \\ \ \\ 7x = 105 \ \\ \ \\ x = 15 \ \\ = 15 \ \text { h }$
$a = \dfrac{ x+5 }{ 40 } = \dfrac{ 15+5 }{ 40 } = \dfrac{ 1 }{ 2 } = 0.5$
$b = \dfrac{ x }{ 30 } = \dfrac{ 15 }{ 30 } = \dfrac{ 1 }{ 2 } = 0.5$

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