To find out how long it will take Michael to complete the entire bike trail, we first understand that in 2 hours he has traveled \( \frac{4}{5} \) of the total distance.
Let \( d \) be the total distance of the bike trail. According to the information given, in 2 hours, Michael travels \( \frac{4}{5}d \).
We can set up a proportion to find out how long it will take him to travel the entire distance \( d \) at the same rate.
The time it takes to travel the complete distance \( d \) can be found as follows:
\[ \frac{4}{5}d \text{ takes 2 hours} \]
To find out how long it takes to travel \( d \), we set up the equation:
\[ d = \frac{5}{4} \times \text{(2 hours)} \]
Calculating that gives:
\[ d = \frac{5}{4} \times 2 = \frac{10}{4} = 2.5 \text{ hours} \]
Thus, the total time it will take him to complete the entire bike trail is \( \boxed{2.5} \) hours.