Reading a map scale

In the corner of the map it says one to fifty thousand. That means one centimetre on the paper is fifty thousand centimetres on the ground, which is five hundred metres.

Scale $1:50000$: $1$ cm on the map is $50000$ cm on the ground, that is $500$ m.

$1:50000\Rightarrow 1\mathrm{cm}=500\mathrm{m}$.

Two bridges are six centimetres apart on the map. Six times five hundred is three thousand metres, so the bridges are three kilometres apart.

Two bridges are $6$ cm apart on the map: $6\times 500=3000$ m, that is $3$ km.

$6\times 500=3000\mathrm{m}$.

Walking at four kilometres an hour, three kilometres takes three quarters of an hour, which is forty-five minutes.

Walking at $4$ km/h: $3÷4=0.75$ h, that is $45$ min.

$3÷4=0.75\mathrm{h}=45^{\prime }$.

A small surprise: areas do not grow like lengths. A square of one centimetre by one centimetre on the map is five hundred metres by five hundred metres on the ground, a quarter of a square kilometre. A field that looks like six square centimetres on the map is really one and a half square kilometres.

Areas do not grow like lengths. $1{\mathrm{cm}}^2$ on the map is $500\times 500=250000$ square metres, that is $0.25$ square kilometres. A field of $6{\mathrm{cm}}^2$ on the map: $6\times 0.25=1.5$ square kilometres.

$1{\mathrm{cm}}^2=500\mathrm{m}\times 500\mathrm{m}=0.25{\mathrm{km}}^2$; $6\times 0.25=1.5{\mathrm{km}}^2$.