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?

Correct result:

x =  15 h
a =  0.5
b =  0.5

Solution:

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

$a=\dfrac{ x+5 }{ 40 }=\dfrac{ 15+5 }{ 40 }=\dfrac{ 1 }{ 2 }=0.5$

$b=\dfrac{ x }{ 30 }=\dfrac{ 15 }{ 30 }=\dfrac{ 1 }{ 2 }=0.5$

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