Calculating Train Distance Using Speed and Time

The problem asks us to find the distance covered by a train given its speed and the time it travels. We are given the train's speed as 120 kmph and the time duration as 15 minutes.

Understanding Speed, Distance, and Time

The relationship between speed, distance, and time is fundamental in physics and mathematics. The formula connecting them is:

• $\text{Distance} = \text{Speed} \times \text{Time}$

To use this formula effectively, the units of speed and time must be consistent. In this case, the speed is in kilometers per hour (kmph), but the time is in minutes. We need to convert the time into hours to match the unit of speed.

Converting Time Units

The given time is 15 minutes. We know that 1 hour is equal to 60 minutes. To convert minutes into hours, we divide the number of minutes by 60.

• Given Time = 15 minutes
• Conversion Factor: $\text{1 hour} = 60 \text{ minutes}$
• Time in hours = $\frac{\text{Time in minutes}}{\text{60}}$
• Time in hours = $\frac{15}{60} \text{ hours}$
• Time in hours = $\frac{1}{4} \text{ hours}$

So, the train travels for $\frac{1}{4}$ of an hour.

Calculating the Distance Covered

Now that we have the speed in kmph and the time in hours, we can use the distance formula:

• Speed = 120 kmph
• Time = $\frac{1}{4}$ hours
• $\text{Distance} = \text{Speed} \times \text{Time}$
• $\text{Distance} = 120 \text{ km/h} \times \frac{1}{4} \text{ h}$

Let's perform the multiplication:

• $\text{Distance} = \frac{120}{4} \text{ km}$
• $\text{Distance} = 30 \text{ km}$

The distance covered by the train in 15 minutes is 30 kilometers.

Comparing with Options

Let's look at the given options:

Our calculated distance of 30 km matches Option 2.

Revision Table: Train Speed, Distance, Time

Additional Information: Speed, Distance, and Time Concepts

Understanding the relationship between speed, distance, and time is crucial for solving many problems in physics and quantitative aptitude. Always ensure the units are consistent before performing calculations. If speed is in km/h, time must be in hours, and distance will be in km. If speed is in m/s, time must be in seconds, and distance will be in meters.

Conversion factors commonly used:

• 1 km = 1000 meters
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3600 seconds

To convert speed from km/h to m/s, multiply by $\frac{5}{18}$. To convert speed from m/s to km/h, multiply by $\frac{18}{5}$.

For example, 120 kmph in m/s is $120 \times \frac{5}{18} = \frac{600}{18} = \frac{100}{3} \text{ m/s}$.

Using these conversions helps in solving problems where different units are provided.