#### Answer

The second car will overtake the first car after 10 hours.

#### Work Step by Step

Let t represent the time it will take the second car to overtake the first car.
Since the second car travels for t time and leaves one hour later than the first car, it means that the first car travels for one hour more, which is equal to t + 1.
For the second car to overtake the first car, it should cover the same distance as the first car.
The first car travels at 50 miles per hour, for t+1 hours and for a distance of 50 $\times$ (t + 1) = 50t + 50.
The second car travels at 55 miles per hour, for t hours and for a distance of 55 $\times$ t = 55t.
Since the distance both cars cover is equal, we solve the following equation:
50t + 50 = 55t
50 = 55t - 50t
50 = 5t
Divide both sides by 5:
t = 10.
The second car will overtake the first car after 10 hours.