Calculating Train Distance at Uniform Speed

The problem asks us to find the distance a train travels given its uniform speed and the time duration. We are given the speed of the train and the time it travels, and we need to calculate the distance covered.

Understanding the Given Information

• Speed of the train: $v = 360 \text{ km/h}$
• Time of travel: $t = 18 \text{ minutes}$

We need to find the distance traveled by the train in 18 minutes.

Formula for Distance, Speed, and Time

The relationship between distance, speed, and time for an object moving at a uniform speed is given by the formula:

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

Or in symbols:

$d = v \times t$

Unit Conversion: Minutes to Hours

Before we can use the formula, we must ensure that the units of speed and time are consistent. The speed is given in kilometers per hour (km/h), but the time is given in minutes. We need to convert the time from minutes to hours.

We know that:

$1 \text{ hour} = 60 \text{ minutes}$

To convert minutes to hours, we divide the number of minutes by 60.

$18 \text{ minutes} = \frac{18}{60} \text{ hours}$

Let's simplify the fraction:

$\frac{18}{60} = \frac{18 \div 6}{60 \div 6} = \frac{3}{10} \text{ hours}$

So, the time of travel in hours is $t = 0.3 \text{ hours}$.

Calculating the Distance Traveled

Now that the time is in hours, we can use the formula $d = v \times t$ with the speed in km/h and time in hours.

Given speed $v = 360 \text{ km/h}$ and time $t = 0.3 \text{ hours}$.

$d = 360 \text{ km/h} \times 0.3 \text{ hours}$

$d = 360 \times \frac{3}{10} \text{ km}$

$d = \frac{360 \times 3}{10} \text{ km}$

$d = \frac{1080}{10} \text{ km}$

$d = 108 \text{ km}$

The train travels 108 km in 18 minutes.

Summary of Calculation Steps

1. Identify the given speed and time.
2. Recognize the need for unit consistency.
3. Convert time from minutes to hours by dividing by 60.
4. Use the formula Distance = Speed × Time.
5. Perform the multiplication to find the distance.

Result

The distance the train will travel in 18 minutes is 108 km.

Revision Table: Speed, Distance, Time Calculations

Additional Information on Uniform Speed Problems

When solving problems involving uniform speed, it is crucial to ensure that the units for speed and time are compatible. If speed is in km/h, time should be in hours for the distance to be in kilometers. If speed is in m/s, time should be in seconds for the distance to be in meters.

Uniform Speed: Uniform speed means that the object is moving at a constant rate, covering equal distances in equal intervals of time, no matter how small the interval.

Unit Conversion: Common conversions needed are between hours and minutes (1 hour = 60 minutes), minutes and seconds (1 minute = 60 seconds), kilometers and meters (1 km = 1000 m).

By carefully converting units and applying the correct formula, we can solve various speed, distance, and time problems.