We are given a problem that can be solved using a linear equation model. To do that, let's remember the general form of a linear equation:

Where "m" is the slope and "b" the y-intercept.
Let "y" be the amount to pay and "x" number of miles. Since the initial charge is $25, this means that b = 25. Since we are told that $0.42 per miles is charged. This means that the total cost is the cost per miles by the number of miles plus the initial cost, that is:

Now we are asked about the cost for 42 miles, that is "x = 42". Replacing in the equation we get:

Therefore, the cost to go to her hotel is $42.64