13. How long is a train which passes a signal in twenty seconds at a speed of \( 108 \mathrm{~km} / \mathrm{h} \) ?

To find the length of the train, we start by converting the speed from kilometers per hour to meters per second. \[ 108 \text{ km/h} = \frac{108 \times 1000}{3600} = 30 \text{ m/s} \] Next, we can calculate the distance the train travels in 20 seconds while passing the signal: \[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Distance} = 30 \text{ m/s} \times 20 \text{ s} = 600 \text{ meters} \] Thus, the length of the train is 600 meters. ### Fun Fact: Did you know that the longest train ever recorded was in 2001 in Australia? It measured a whopping 7.3 kilometers! That’s like combining over 1000 standard train cars into one massive rail-spectacle! ### Real-World Application: Trains are vital in many countries for transporting goods and people. Knowing how to calculate the length of a train by its speed or the time it takes to pass a point helps in planning schedules and managing rail networks efficiently. It's super handy when ensuring trains run on time and keeping safety protocols in check!