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

Options

A. 35km/h
B. 37.5km/h
C. 39.5km/h
D. 40.5km/h

Answer

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

### Step 1: Calculate the Total Distance
The train covers two segments of its journey:
- The first segment is 5 km.
- The second segment is 15 km.

**Total Distance = Distance1 + Distance2 = 5 km + 15 km = 20 km**

### Step 2: Calculate the Time Taken for Each Segment
To find the average speed, we need to calculate the time taken for each segment of the journey.

**For the first segment (5 km at 30 km/hr):**
- Time = Distance / Speed
- Time1 = 5 km / 30 km/hr = 1/6 hours

**For the second segment (15 km at 45 km/hr):**
- Time = Distance / Speed
- Time2 = 15 km / 45 km/hr = 1/3 hours

### Step 3: Calculate the Total Time Taken
Now, we will add the time taken for both segments to find the total time.

**Total Time = Time1 + Time2**
- Total Time = (1/6) hours + (1/3) hours

To add these fractions, we need a common denominator:
- The common denominator of 6 and 3 is 6.
- Convert (1/3) to sixths: (1/3) = (2/6).

Now we can add:
- Total Time = (1/6) + (2/6) = 3/6 = 1/2 hours

### Step 4: Calculate the Average Speed
The average speed is given by the formula:

**Average Speed = Total Distance / Total Time**

Substituting the values we calculated:
- 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**.

---