I found a different answer for (b).
To find the solution, we frame all our statements in mathematical language. Suppose that we measure distance from the location at which your car begins accelerating, using to denote your car's distance and to denote the other car's distance. Based on the information given, two equations hold:
I'm not sure if you've learned integration yet, but we can show from these facts that
where is your initial velocity at the moment you begin accelerating and is the initial distance of the other car. You are correct that it takes seconds to accelerate to the speed of the other car. Now, we ask: what is if ?
Similarly, what must be in order that ? How long would it take for the other car to make it that far past you?