A study in measurements, part 4

Algebra Level pending

A velocity of 5 rods per hour is equal to how many furlongs per fortnight?

[1 rod = 198 inches]

[8 furlongs = 1 mile]


The answer is 42.

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2 solutions

Note that:

1 rod = 198 inches

1 feet = 12 inches

1 mile = 5280 feet

8 furlongs = 1 mile

1 day = 24 hours

1 fortnight = 14 days

Then,

5 r o d s h o u r ( 198 i n 1 r o d ) ( 1 f t 12 i n ) ( 1 m i l e 5280 f t ) ( 8 f u r l o n g s 1 m i l e ) ( 24 h r 1 d a y ) ( 14 d a y s 1 f o r t n i g h t ) = 5 \dfrac{rods}{hour}\left(\dfrac{198~in}{1~rod}\right)\left(\dfrac{1~ft}{12~in}\right)\left(\dfrac{1~mile}{5280~ft}\right)\left(\dfrac{8~furlongs}{1~mile}\right)\left(\dfrac{24~hr}{1~day}\right)\left(\dfrac{14~days}{1~fortnight}\right)= 42 f u r l o n g s f o r t n i g h t \color{#D61F06}\boxed{42 \dfrac{furlongs}{fortnight}}

Denton Young
Jul 13, 2017

1 rod = 16.5 feet

1 furlong = 660 feet = 40 rods

1 fortnight = 14 days = 336 hours

So 5 rods per hour = 5 * (336/40) = 42 furlongs per fortnight.

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