A delivery truck travels from City A to City B at an initial speed of 80 km/h. After completing the first 120 km of the route, the driver decreases the speed by 12.5% and finishes the entire trip in a total time of 5.5 hours. How long would the total journey take if the speed reduction had occurred after driving for two hours instead?

The correct option is 5$\frac{3}{7}$ hours.

Step 1: Calculate the time spent driving at the initial speed in the original scenario.
The delivery truck travels at an initial speed of 80 km/h. The time taken to cover the first 120 km is:

$\text{Time}=\frac{120}{80}=1.5\text{hours}$

Step 2: Determine the reduced speed.
The driver decreases the speed by 12.5%. The reduced speed is calculated as:

$\text{Reduced Speed}=80\times (1-0.125)=80\times 0.875=70\text{km/h}$

Step 3: Calculate the total distance between City A and City B.
The total journey took 5.5 hours in the original scenario. The time spent traveling at the reduced speed of 70 km/h is:

$5.5-1.5=4\text{hours}$

The distance covered during these 4 hours is:

$\text{Distance}=70\times 4=280\text{km}$

Thus, the total distance of the trip from City A to City B is:

$\text{Total Distance}=120+280=400\text{km}$

Step 4: Calculate the total journey time for the second scenario.
If the speed reduction occurs after driving for 2 hours at the initial speed of 80 km/h, the distance covered in the first 2 hours is:

$\text{Distance}=80\times 2=160\text{km}$

The remaining distance to be covered at the reduced speed of 70 km/h is:

$\text{Remaining Distance}=400-160=240\text{km}$

The time required to cover the remaining 240 km is:

$\text{Remaining Time}=\frac{240}{70}=\frac{24}{7}=3\frac{3}{7}\text{hours}$

Therefore, the total time for the journey would be:

$\text{Total Time}=2+3\frac{3}{7}=5\frac{3}{7}\text{hours}$