A 600-metre-long train is running at a speed of 48 km/h. It crosses a platform completely in 4 minutes and 30 seconds. What is the length of the platform?

A 600-metre-long train is running at a speed of 48 km/h.

length of train = 600 metre

Speed = 48 km/h = $$\frac{48000}{3600}$$ m/s

= $$\frac{40}{3}$$ m/s

Train crosses a platform completely in 4 minutes and 30 seconds.

4 minutes and 30 seconds = $$(4\times60+30)$$ seconds = (240+30) seconds = 270 seconds

Let's assume the length of the platform is 'y' metre.

$$speed=\frac{length\ of\ train+length\ of\ platform}{time}$$

$$\frac{40}{3}=\frac{600+y}{270}$$

$$40=\frac{600+y}{90}$$
3600 = 600+y
y = 3600-600
length of the platform = y = 3000 m