Minimum distance between two perpendicular moving vehicles

[KNT]

Homework Statement

What is the minimum distance between two vehicles moving perpendicularly toward each other?

Relevant Equations

d = vt

Below is my solution, which I'm not sure is correct. Hopefully the picture shows clearly what I'm trying to find.

 

[Highway_Dylan]

Looks good to me. You can also see that the limits $v_1\rightarrow 0$ and $v_2\rightarrow 0$ make sense.

 

[sepcurio]

If you read the question literally, the answer is obvious. But I don't think that's the answer they're looking for.

Hint: