Ivanna will rent a car for the weekend. she can choose one of two plans. the first plan has an initial fee of $40 and costs an additional $0.16 per mile driven. the second plan has an initial fee of $51 and costs an additional $0.11 per mile driven. for what amount of driving do the two plans cost the same? (miles) what is the cost when the two plans cost the same? (dollars)

First, let's make these two into equations.
The first plan has an initial fee of $40 and costs an additional $0.16 per mile driven.
Our equation would then be
C = 40 + 0.16m
where C is the total cost, and m is the number of miles driven.
The second plan has an initial fee of $51 and costs an additional $0.11 per mile driven.
So, the equation is
C = 51 + 0.11m
where C is the total cost, and m is the number of miles driven.
Now, your question seems to be asking for one mileage for both, equalling one cost. I would go through all the steps I've taken to try and find this for you, but it would probably take hours to type out and read. In short, I'm not entirely sure that an answer like that is possible in this situation, simply because of the large difference in the initial fee of the two plans, along with the sparse common multiples between the two mileage costs.