# Excavation

Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end.

On what day since the beginning of excavation they met?

Result

n =  8

#### Solution:

$\dfrac{ 3}{ 12}+\dfrac{ n-3}{ 12} + \dfrac{ n-3}{ 10} = 1 \ \\ \ \\ n = 3 + (1-\dfrac{ 3}{ 12})\cdot \dfrac{ 12 \cdot 10 }{ 12 + 10} \doteq 8$

3 / 12 +(n-3)/12 + (n-3)/10 = 1

11n = 78

n = 7811 ≈ 7.090909

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