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⋅ (1/40+1/30)+5/40=1  7x=105  x=15 =15  h  \ \\ x \cdot \ (1/40+1/30) + 5/40 = 1 \ \\ \ \\ 7x = 105 \ \\ \ \\ x = 15 \ \\ = 15 \ \text { h }
a=x+540=15+540=12=0.5a = \dfrac{ x+5 }{ 40 } = \dfrac{ 15+5 }{ 40 } = \dfrac{ 1 }{ 2 } = 0.5
b=x30=1530=12=0.5b = \dfrac{ x }{ 30 } = \dfrac{ 15 }{ 30 } = \dfrac{ 1 }{ 2 } = 0.5

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