The ratio of the speeds of two trains is 5 : 8. If the second train runs 600 km in 4 hours, then the speed of the first train (in km/h) is:

Options

A. 25.5
B. 62.5
C. 37.75
D. 93.75

Answer

To solve the problem, we need to find the speed of the first train given the ratio of the speeds of two trains and the speed of the second train.

### Step-by-Step Solution:

1. **Understand the ratio of speeds**: The ratio of the speeds of the two trains is given as 5:8. This means if the speed of the first train is 5x, then the speed of the second train is 8x, where x is a common multiplier.

**Hint**: Remember that ratios can be expressed in terms of a variable to make calculations easier.

2. **Calculate the speed of the second train**: We know that the second train runs 600 km in 4 hours. To find its speed, we use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{600 \text{ km}}{4 \text{ hours}} = 150 \text{ km/h} \]

**Hint**: Use the formula for speed (Distance/Time) to find the speed of any object.

3. **Set up the equation using the ratio**: From the ratio, we have:
\[ 8x = 150 \text{ km/h} \]
To find x, we can rearrange the equation:
\[ x = \frac{150}{8} = 18.75 \]

**Hint**: Isolate the variable by dividing both sides of the equation by the coefficient of x.

4. **Find the speed of the first train**: Now that we have the value of x, we can find the speed of the first train:
\[ \text{Speed of the first train} = 5x = 5 \times 18.75 = 93.75 \text{ km/h} \]

**Hint**: Substitute the value of x back into the expression for the first train's speed to find the answer.

### Final Answer:
The speed of the first train is **93.75 km/h**.