Bob and Carl each rented the same kind of moving truck from EZ Move. There was a flat rental fee plus a charge per mile that the truck was driven. Bob’s cost for his truck was $112.96 for 138 miles. Carl’s cost for his truck was $142.78 for 209 miles. Which equation can be used to represent the cost of the rental truck?

To find the cost equation that represents the rental truck situation, we can set up a system of equations based on the provided information.

Let's denote:
- \( y \) as the total cost of the rental truck,
- \( x \) as the number of miles driven,
- \( f \) as the flat rental fee,
- \( c \) as the charge per mile.

From Bob's rental, we can create the equation:
\[
112.96 = f + 138c \quad (1)
\]

From Carl's rental, we have:
\[
142.78 = f + 209c \quad (2)
\]

Now, let's subtract equation (1) from equation (2):
\[
(142.78 - 112.96) = (f + 209c) - (f + 138c)
\]
\[
29.82 = 71c
\]

Now, solving for \( c \) (the charge per mile):
\[
c = \frac{29.82}{71} \approx 0.42
\]

Now, we can substitute \( c \) back into either equation to find \( f \). Let's use equation (1):
\[
112.96 = f + 138(0.42)
\]
\[
112.96 = f + 57.96
\]
\[
f = 112.96 - 57.96 = 55
\]

Therefore, we have:
- The flat fee \( f \) is approximately 55,
- The charge per mile \( c \) is approximately 0.42.

Thus, the cost equation can be represented as:
\[
y = 0.42x + 55
\]

The correct answer from the options provided is:
\[
\boxed{y = 0.42x + 55}
\]