Sure! To find the distance traveled by the train, we can follow a few simple steps:
1. Convert the given time into hours:
- We know the train travels for one-quarter of a minute.
- A quarter of a minute equals [tex]\( \frac{1}{4} \)[/tex] minute, which is [tex]\( 0.25 \)[/tex] minutes.
- Since there are 60 minutes in an hour, we need to convert the time from minutes to hours by dividing the time in minutes by 60.
[tex]\[
\text{Time in hours} = \frac{0.25}{60} \text{ hours}
\][/tex]
2. Calculate the distance traveled using the speed-time relationship:
- The speed of the train is 54 kilometers per hour ([tex]\( \text{km/hr} \)[/tex]).
- The relationship between distance, speed, and time is given by the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
- With a speed of 54 km/hr and the time in hours (calculated above):
[tex]\[
\text{Distance} = 54 \, (\text{km/hr}) \times 0.004166666666666667 \, (\text{hours})
\][/tex]
3. Compute the distance:
- Multiplying the speed by the time:
[tex]\[
\text{Distance} = 54 \text{ km/hr} \times 0.004166666666666667 \text{ hours} = 0.225 \text{ km}
\][/tex]
So, the train travels a distance of [tex]\( 0.225 \)[/tex] kilometers in one-quarter of a minute (0.25 minutes).
