A train covers the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. What is the average speed of the train?

Options

A. 35km/hr
B. 37.5km/hr
C. 39.5km/hr
D. 40km/hr

Explanation

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

### Step 1: Calculate the time taken for the first part of the journey.
The train covers the first 5 km at a speed of 30 km/hr.

- **Time = Distance / Speed**
- Time for the first 5 km = 5 km / 30 km/hr = 1/6 hours.

### Step 2: Calculate the time taken for the second part of the journey.
The train covers the next 15 km at a speed of 45 km/hr.

- Time for the next 15 km = 15 km / 45 km/hr = 1/3 hours.

### Step 3: Calculate the total distance covered.
The total distance covered by the train is:

- Total Distance = Distance of first part + Distance of second part = 5 km + 15 km = 20 km.

### Step 4: Calculate the total time taken.
Now, we need to add the time taken for both parts of the journey:

- Total Time = Time for first part + Time for second part = (1/6) hours + (1/3) hours.

To add these fractions, we need a common denominator:

- (1/3) = (2/6), so:
- Total Time = (1/6) + (2/6) = (3/6) = 1/2 hours.

### Step 5: Calculate the average speed.
The average speed is given by the formula:

- **Average Speed = Total Distance / Total Time**
- Average Speed = 20 km / (1/2 hours) = 20 km * (2/1) = 40 km/hr.

### Final Answer:
The average speed of the train is **40 km/hr**.

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