How fast is the train?

The train is two hundred metres long, and it takes eight seconds to pass a signal post beside the track. So in one second it travels twenty-five metres.

The train is $200$ m long and passes a post in $8$ s. Speed: $v=\frac{d}{t}=200÷8=25$ m/s.

$d=200\mathrm{m}$ and $t=8\mathrm{s}$: $v=\frac{d}{t}=25m/s$.

An hour has three thousand six hundred seconds and a kilometre has a thousand metres. To turn metres per second into kilometres per hour you multiply by three point six. Twenty-five times three point six is ninety.

$1$ h $=3600$ s and $1$ km $=1000$ m. To turn m/s into km/h: $3600÷1000=3.6$. So $25\times 3.6=90$ km/h.

$\frac{3600}{1000}=3.6$ and $25\times 3.6=90km/h$.

Passengers have a trick. The posts beside the track stand fifty metres apart. Count ten posts in twenty seconds and the train has gone five hundred metres, which is again twenty-five metres every second.

A trick: posts stand $50$ m apart. Count $10$ posts in $20$ s: $10\times 50=500$ m, and $500÷20=25$ m/s. The same answer.

posts $50\mathrm{m}$ apart: $\frac{10\times 50}{20}=25m/s$.

A journey of a hundred and eighty kilometres at ninety kilometres an hour takes exactly two hours: time enough to count a great many posts.

$180$ km at $90$ km/h: $180÷90=2$ h. Time enough to count a great many posts.

$\frac{180}{90}=2\mathrm{h}$.