On a map with a scale of 1 : 300 000 the distance between Burnley and Blackburn
is 5.5 cm.
(a) Find the distance between the two towns in km.
(b) How far apart would the two towns be on a map with a scale of 1 : 50 000?

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Solution

Dear Student,

$o n t h e m a p 1 c m r e p r e s e n t 300000 c m h e n c e 5.5 c m r e p r e s e n t s = 5.5 \times 300000 = 16, 50, 000 c m d i s \tan c e i n k m 1 k m = 1000 m t e r e 1 m e t e r = 100 c m h e n c e 1 k m = 100 \times 1000 c m = 100000 c m 100000 c m = 1 k m 16, 50, 000 c m = \frac{1}{100000} \times 16, 50, 000 = \frac{165}{10} = 16.5 k m$

b)
when the scale is 1:50000
then the two cities are
$1 c m r e p r e s e n t s 50000 c m a s t h e c i t i e s a r e 16, 50000 c m a p a r t h e n c e o n t h e m a p t h e y w i l l b e \frac{1650000}{50000} = 33 c m H e n c e t h e t w o t o w n s w i l l b e 33 c m a p a r t .$

Regards,

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