A goods train in five successive minutes from its starts runs 68 metres, 127 metres, 208 metres,312 metres and 535 metres and for the next 5 minutes maintains an average speed of 33 km/hr. find the average speed of the train in km/hr in covering this total distance.

Options

A. 20 km/hr
B. 30 km/hr
C. 28 km/hr
D. 24 km/hr

Answer

To find the average speed of the goods train over the total distance covered, we can follow these steps:

### Step 1: Calculate the total distance covered in the first 5 minutes.
The distances covered in the first 5 minutes are:
- 68 meters
- 127 meters
- 208 meters
- 312 meters
- 535 meters

**Total distance for the first 5 minutes:**
\[ \text{Total distance} = 68 + 127 + 208 + 312 + 535 \]
\[ \text{Total distance} = 1250 \text{ meters} \]

### Step 2: Convert the distance from meters to kilometers.
Since 1 kilometer = 1000 meters, we convert the total distance:
\[ \text{Total distance in km} = \frac{1250}{1000} = 1.25 \text{ km} \]

### Step 3: Calculate the distance covered in the next 5 minutes.
The average speed during the next 5 minutes is given as 33 km/hr.

**Convert 5 minutes to hours:**
\[ \text{Time in hours} = \frac{5}{60} = \frac{1}{12} \text{ hours} \]

**Calculate the distance using the formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 33 \text{ km/hr} \times \frac{1}{12} \text{ hr} = \frac{33}{12} = 2.75 \text{ km} \]

### Step 4: Calculate the total distance covered.
Now, we can find the total distance covered by adding the distances from both segments:
\[ \text{Total distance} = 1.25 \text{ km} + 2.75 \text{ km} = 4 \text{ km} \]

### Step 5: Calculate the total time taken.
The total time taken for the journey is:
\[ \text{Total time} = 10 \text{ minutes} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \]

### Step 6: Calculate the average speed.
Using the formula for average speed:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]
\[ \text{Average speed} = \frac{4 \text{ km}}{\frac{1}{6} \text{ hours}} = 4 \times 6 = 24 \text{ km/hr} \]

### Final Answer:
The average speed of the train over the total distance is **24 km/hr**.

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