To find out how long it will take Michael to complete the entire bike trail, we can start by determining his biking rate and then use that to find the total time for the entire distance.
Michael has biked \( \frac{4}{5} \) of the total distance in 2 hours.
To find his rate, we first set up the scenario:
Let \( D \) be the total distance of the bike trail. The distance he has already biked is \( \frac{4}{5}D \).
Now, if it took him 2 hours to bike \( \frac{4}{5}D \), we can calculate his biking rate: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{4}{5}D}{2 \text{ hours}} = \frac{4}{10}D = \frac{2}{5}D \text{ per hour} \]
To find the total time \( T \) it will take him to travel the entire distance \( D \), we can use the rate: \[ D = \text{Rate} \times \text{Time} \] \[ D = \frac{2}{5}D \times T \]
We can solve for \( T \) by dividing both sides by \( D \) (assuming \( D \neq 0 \)): \[ 1 = \frac{2}{5} T \]
Now, to find \( T \): \[ T = \frac{5}{2} \text{ hours} \]
Converting \( \frac{5}{2} \) hours into hours and minutes gives us: \[ \frac{5}{2} \text{ hours} = 2.5 \text{ hours} = 2 \text{ hours and } 30 \text{ minutes} \]
Now we can find the total time including the first 2 hours: So, the total time to complete the entire bike trail will be: \[ 2 \text{ hours} + 2.5 \text{ hours} = 4.5 \text{ hours} \]
Thus, the total time it will take him to complete the entire bike trail is 4.5 hours or 4 hours and 30 minutes.
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