$\"\"$

The average speed of the truck while going is $\"x\"$ mph.

The average speed of the truck while returning is $\"y\"$ mph.

The average speed for the total trip is $\"50\"$ mph.

Distance to be travel by the truck to reach the city is $\"d\"$ miles.

Total Distance travelled by the truck is $\"d+d=2d\"$ .

$\"\\textup{\\textrm{time}}=\\frac{\\textup{\\textrm{distance}}}{\\textup{\\textrm{speed}}}\"$ .

The time taken by the truck to reach the city is $\"t_{1}=\\frac{d}{x}\"$ .

The time taken by the truck while returning back from the city is $\"t_{2}=\\frac{d}{y}\"$ .

$\"\"$

The total time taken by the truck is $\"t_{1}+t_{2}=\\frac{2d}{50}\"$ .

$\"t_{1}+t_{2}=\\frac{2d}{50}\"$

$\"\\frac{d}{x}+\\frac{d}{y}=\\frac{2d}{50}\"$

$\"\\frac{1}{x}+\\frac{1}{y}=\\frac{2}{50}\"$

Multiply each side by $\"xy\"$ .

$\"xy\\left$

$\"y+x=\\frac{1}{25}xy\"$

$\"\\\\25(y+x)=xy$

The domain of function is all possible values of $\"x\"$ .

Denominator of the function should not be zero.

$\"x-25\\neq$

$\"x\\neq$ .

The Domain is $\"\\left\\{$ .

$\"\"$

(b)

Draw the table for different values.

$\"x\"$	$\"30\"$	$\"40\"$	$\"50\"$	$\"60\"$
$\"y\"$	$\"150\"$	$\"66.667\"$	$\"50\"$	$\"42.857\"$

Observe the table

The $\"x\"$ comes closer to $\"25\"$ , the value of $\"y\"$ becomes very large.

$\"\"$

(c)

$\"\\lim_{x\\rightarrow$

As $\"x\"$ tends to $\"25\"$ from the right hand side, the function approaches to $\"\\infty\"$ .

$\"\\lim_{x\\rightarrow$ .

$\"\"$

(a) $\"y=\\frac{25x}{x-25}\"$ .

Domain is $\"\\left\\{$

(b)

$\"x\"$	$\"30\"$	$\"40\"$	$\"50\"$	$\"60\"$
$\"y\"$	$\"150\"$	$\"66.667\"$	$\"50\"$	$\"42.857\"$