$\displaystyle a, b, c$ are positive real numbers.

If they satisfy the equations:

$\displaystyle (\frac{b}{a}+\frac{a}{b})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{70}{a+b+c}$

$\displaystyle (\frac{c}{b}+\frac{b}{c})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{90}{a+b+c}$

$\displaystyle (\frac{a}{c}+\frac{c}{a})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{110}{a+b+c}$

Find the value of

$\displaystyle (a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$.