Step 1 :Given the cost function $C = 75d + 0.4k$, where $C$ is the total cost, $d$ is the number of days rented, and $k$ is the number of kilometers driven.
Step 2 :Toni has $\$ 340$ to spend on a car for 3 days, so we have $C = 340$ and $d = 3$.
Step 3 :Substitute the values of $C$ and $d$ into the cost function: $340 = 75(3) + 0.4k$.
Step 4 :Solve for $k$: $340 = 225 + 0.4k$.
Step 5 :Subtract 225 from both sides: $115 = 0.4k$.
Step 6 :Divide both sides by 0.4: $k = \frac{115}{0.4}$.
Step 7 :Calculate the value of $k$: $k = 287.5$.
Step 8 :\(\boxed{k = 287.5}\) kilometers is the total distance Toni can travel.