A 280 m long train running at a speed of 72 km/hr passes a platform in 30 seconds. Find the length of the platform (in m).
320
Here's how to solve this problem step-by-step:
1. Convert units:
The train's speed is given in km/hr, but we need it in m/s to match the time given in seconds. There are 1000 meters in a kilometer and 3600 seconds in an hour. Therefore:
\(72 \frac{km}{hr} \times \frac{1000 m}{1 km} \times \frac{1 hr}{3600 s} = 20 \frac{m}{s}\)
2. Calculate the total distance covered:
The train covers the length of the platform plus its own length in 30 seconds. We know its speed (20 m/s) and the time (30 s), so we can calculate the total distance:
\(Distance = Speed \times Time = 20 \frac{m}{s} \times 30 s = 600 m\)
3. Find the platform's length:
The total distance covered (600 m) includes the length of the train (280 m) and the length of the platform (let's call it 'x'). Therefore:
\(280 m + x = 600 m\)
Solving for x:
\(x = 600 m - 280 m = 320 m\)
Therefore, the length of the platform is 320 meters.
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