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?

Correct Answer: 5$\frac{3}{7}$ hours

Step-by-Step Explanation:

Step 1: Find the time taken for the first segment of the trip.

The truck starts at a speed of 80 km/h and covers the first 120 km at this speed.

Using the formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

$t_1=\frac{120\text{km}}{80\text{km/h}}=1.5\text{hours}$

Step 2: Calculate the reduced speed and total distance of the trip.

After 120 km, the speed is reduced by 12.5%.

Speed reduction = $80\times 12.5\%=80\times 0.125=10\text{km/h}$

New reduced speed ($v_2$):

$v_2=80-10=70\text{km/h}$

Since the total trip took 5.5 hours, the time spent driving at the reduced speed ($t_2$) is:

$t_2=5.5-1.5=4\text{hours}$

Distance covered during this second segment ($d_2$):

$d_2=70\text{km/h}\times 4\text{hours}=280\text{km}$

Total distance between City A and City B ($D$):

$D=120\text{km}+280\text{km}=400\text{km}$

Step 3: Analyze the new scenario where speed reduction occurs after 2 hours.

If the driver maintains the initial speed of 80 km/h for 2 hours, the distance covered is:

$d_{\text{new,1}}=80\text{km/h}\times 2\text{hours}=160\text{km}$

Remaining distance of the journey:

$d_{\text{remaining}}=400\text{km}-160\text{km}=240\text{km}$

Time required to complete the remaining distance at the reduced speed of 70 km/h:

$t_{\text{remaining}}=\frac{240\text{km}}{70\text{km/h}}=\frac{24}{7}=3\frac{3}{7}\text{hours}$

Step 4: Calculate total journey time for the new scenario.

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