Calculating Train Travel Time

This solution explains how to find the time taken for a train to cover a specific distance at a given speed.

Step 1: Convert Speed Units

The distance is given in kilometers (km), but the speed is in meters per second (m/s). To use the standard formula relating distance, speed, and time, we need consistent units. We will convert the speed from m/s to kilometers per hour (km/h).

• The conversion factor from m/s to km/h is $\frac{18}{5}$.
• Given speed = $20$ m/s.
• Speed in km/h = $20 \times \frac{18}{5}$ km/h.
• Speed = $4 \times 18$ km/h = $72$ km/h.

Step 2: Calculate Time Taken

The relationship between distance ($d$), speed ($v$), and time ($t$) is given by the formula:

$ t = \frac{d}{v} $

• Distance ($d$) = $360$ km.
• Speed ($v$) = $72$ km/h.
• Time ($t$) = $\frac{360 \text{ km}}{72 \text{ km/h}}$.
• Time ($t$) = $5$ hours.

Therefore, the time taken to cover the distance is 5 hours.