Answer
$T(x)=\frac{720x+48050}{(x+70)(x+65)}$.
$T(0)=11$.
Work Step by Step
The given function is
$\Rightarrow T(x)=\frac{470}{x+70}+\frac{250}{x+65}$.
The LCD of the denominators is $(x+70)(x+65)$.
Multiply the numerators and the denominators
$\Rightarrow T(x)=\frac{470(x+65)}{(x+70)(x+65)}+\frac{250(x+70)}{(x+70)(x+65)}$
Add both numerators because denominators are equal.
$\Rightarrow T(x)=\frac{470(x+65)+250(x+70)}{(x+70)(x+65)}$
$\Rightarrow T(x)=\frac{470x+30550+250x+17500}{(x+70)(x+65)}$
Add like terms.
$\Rightarrow T(x)=\frac{720x+48050}{(x+70)(x+65)}$
Replace $x$ with $0$.
$\Rightarrow T(0)=\frac{720(0)+48050}{(0+70)(0+65)}$
Simplify.
$\Rightarrow T(0)=\frac{48050}{(70)(65)}$
$\Rightarrow T(0)=\frac{48050}{4550}$
$\Rightarrow T(0)=10.5604395604$
Rounded to the nearest hour.
$\Rightarrow T(0)=11$
