Evaluate: $15\frac{1}{3}\%$ of 480 km + $58\frac{1}{3}\%$ of 300 km

The correct answer is 248.6 km.

To evaluate the given expression step-by-step, we will break it down into two parts, calculate each term, and then add the results together.

Step 1: Convert the mixed fractions to improper fractions.

First fraction:
$15\frac{1}{3}\%$ = $\frac{15\times 3+1}{3}\%=\frac{46}{3}\%$

Second fraction:
$58\frac{1}{3}\%$ = $\frac{58\times 3+1}{3}\%=\frac{175}{3}\%$

Step 2: Calculate the value of the first part ($15\frac{1}{3}\%$ of 480 km).

$\frac{46}{3}\%\times 480=\frac{46}{3\times 100}\times 480$

Simplify by dividing 480 by 3:
$\frac{480}{3}=160$

Now substitute back into the expression:
$\frac{46\times 160}{100}=\frac{7360}{100}=73.6\text{km}$

Step 3: Calculate the value of the second part ($58\frac{1}{3}\%$ of 300 km).

$\frac{175}{3}\%\times 300=\frac{175}{3\times 100}\times 300$

Simplify by dividing 300 by 300:
$\frac{3\times 100}{3\times 100}=1$

So, the second part equals:
$175\text{km}$

Step 4: Add both results together.

$\text{Total}=73.6\text{km}+175\text{km}=248.6\text{km}$

Therefore, the final value is 248.6 km.