A train runs for 2 hrs at the speed of 40 km/h and then runs for `4(1)/(2)` hrs at the speed of 60 km/h and then runs for `3(1)/(2)` hrs, at the speed of 70 km per hour. Find the average speed of the train.

Options

A. 59.5 km/h
B. 80km/h
C. 56.87 km/h
D. 57.1 km/h

Explanation

To find the average speed of the train, we need to follow these steps:

### Step 1: Calculate the distance covered in each segment of the journey.

1. **First Segment**:
- Time = 2 hours
- Speed = 40 km/h
- Distance = Speed × Time = 40 km/h × 2 h = 80 km

2. **Second Segment**:
- Time = 4.5 hours (which is 4 hours and 30 minutes)
- Speed = 60 km/h
- Distance = Speed × Time = 60 km/h × 4.5 h = 270 km

3. **Third Segment**:
- Time = 3.5 hours (which is 3 hours and 30 minutes)
- Speed = 70 km/h
- Distance = Speed × Time = 70 km/h × 3.5 h = 245 km

### Step 2: Calculate the total distance covered.

Total Distance = Distance from First Segment + Distance from Second Segment + Distance from Third Segment
Total Distance = 80 km + 270 km + 245 km = 595 km

### Step 3: Calculate the total time taken.

Total Time = Time from First Segment + Time from Second Segment + Time from Third Segment
Total Time = 2 h + 4.5 h + 3.5 h = 10 h

### Step 4: Calculate the average speed.

Average Speed = Total Distance / Total Time
Average Speed = 595 km / 10 h = 59.5 km/h

Thus, the average speed of the train is **59.5 km/h**.

---