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The problem states that a train at a uniform speed covers a distance of 255 km in 1\(\frac{1}{2}\) hours, and it asks to find the speed of the train and the distance it would cover in 3\(\frac{4}{5}\) hours.

Let's break this down step by step:

### 1. Calculate the speed of the train:
- The formula for speed is given by:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
- Distance = 255 km
- Time = 1\(\frac{1}{2}\) hours = 1.5 hours

\[
\text{Speed} = \frac{255 \text{ km}}{1.5 \text{ hours}} = 170 \text{ km/h}
\]

### 2. Calculate the distance covered in 3\(\frac{4}{5}\) hours:
- First, convert 3\(\frac{4}{5}\) hours to a decimal:
\[
3\frac{4}{5} = 3 + \frac{4}{5} = 3.8 \text{ hours}
\]
- Now, using the speed of 170 km/h, we can calculate the distance:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 170 \text{ km/h} \times 3.8 \text{ hours} = 646 \text{ km}
\]

### Final answers:
- Speed of the train = **170 km/h**
- Distance covered in 3\(\frac{4}{5}\) hours = **646 km**

Would you like more details or have any questions?

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Here are five related questions for further practice:
1. If the train had traveled for 2.5 hours, how far would it have gone?
2. How long would it take the train to travel 510 km at the same speed?
3. If the speed of the train decreased by 20 km/h, what would be the new time taken to cover 255 km?
4. How far would the train travel in 5 hours if its speed increased by 10%?
5. What would the speed be if the train covered 200 km in 1.25 hours?

**Tip:** Always convert mixed fractions to decimals when working with time or distances for easier calculations!

A train at a uniform speed covers a distance of 255 km in 1 1/2 hours. Find the speed of the train and the distance covered in 3 4/5 hours.

Calculate the speed of a train that covers 255 km in 1 1/2 hours, and find the distance it will cover in 3 4/5 hours using the formula Speed = Distance / Time. This problem teaches key mathematical concepts of distance and time relationships, suitable for students in Grades 7-9.

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