A freight train covers a distance of 120 km at a speed of 40 km/h, another 150 km at 50 km/h, and a final segment of 80 km at 80 km/h. Determine the average speed of the train for the entire journey.

The correct option is 50 km/h.

Step 1: Understand the formula for Average Speed
Average speed for a journey consisting of multiple segments is defined as the total distance covered divided by the total time taken for the entire trip.

$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

Step 2: Calculate the time taken for each segment of the journey
Using the time-distance-speed formula:
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

For the first segment (120 km at 40 km/h):
${\text{Time}}_1=\frac{120\text{km}}{40\text{km/h}}=3\text{hours}$

For the second segment (150 km at 50 km/h):
${\text{Time}}_2=\frac{150\text{km}}{50\text{km/h}}=3\text{hours}$

For the third segment (80 km at 80 km/h):
${\text{Time}}_3=\frac{80\text{km}}{80\text{km/h}}=1\text{hour}$

Step 3: Calculate the Total Distance and Total Time
Total Distance:
$\text{Total Distance}=120+150+80=350\text{km}$

Total Time:
$\text{Total Time}=3+3+1=7\text{hours}$

Step 4: Compute the Average Speed
Now, substitute the total distance and total time into the average speed formula:

$\text{Average Speed}=\frac{350\text{km}}{7\text{hours}}=50\text{km/h}$

Thus, the average speed of the freight train for the entire journey is 50 km/h.