A train covers 108 km in first two hours ,36 km in next half an hour and 90 km in next two hours .Find the average speed of the train during the whole journey.

Answer

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

### Step 1: Calculate Total Distance
First, we need to find the total distance covered by the train during its journey.

- Distance covered in the first two hours: 108 km
- Distance covered in the next half an hour: 36 km
- Distance covered in the next two hours: 90 km

**Total Distance = 108 km + 36 km + 90 km**

**Total Distance = 234 km**

### Step 2: Calculate Total Time
Next, we need to calculate the total time taken for the journey.

- Time for the first part: 2 hours
- Time for the second part: 0.5 hours (which is half an hour)
- Time for the third part: 2 hours

**Total Time = 2 hours + 0.5 hours + 2 hours**

**Total Time = 4.5 hours**

### Step 3: Calculate Average Speed
Now we can calculate the average speed using the formula:

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

Substituting the values we found:

**Average Speed = 234 km / 4.5 hours**

### Step 4: Simplify the Calculation
To make the division easier, we can multiply both the numerator and the denominator by 10 to eliminate the decimal:

**Average Speed = (234 * 10) / (4.5 * 10)**

**Average Speed = 2340 / 45**

Now, we can simplify this fraction:

1. Divide both the numerator and denominator by 5:
- 2340 ÷ 5 = 468
- 45 ÷ 5 = 9

So we have:

**Average Speed = 468 / 9**

2. Now divide 468 by 9:
- 468 ÷ 9 = 52

### Final Answer
Thus, the average speed of the train during the whole journey is **52 km/h**.

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