Answer
$ T(x)=\frac{720x+48050}{(x+70)(x+65)}$.
$T(5)=10$.
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 $5$.
$\Rightarrow T(5)=\frac{720(5)+48050}{(5+70)(5+65)}$
Simplify.
$\Rightarrow T(5)=\frac{3600+48050}{(75)(70)}$
$\Rightarrow T(5)=\frac{51650}{5250}$
$\Rightarrow T(5)=9.8380952381$
Rounded to the nearest hour:
$\Rightarrow T(5)=10$.
