If you go 100 furlongs in a fortnight how many miles per hour does that equal?
I know there are 200 yards in a furlong and 1760 yards in a mile and 14 days
in a fortnight. Now I don't know what step to take.
Write 100 furlongs/fortnight as:
100 furlongs
------------
1 fortnight
Now to cancel away furlongs in the numerator, create a fraction
which equals 1 that has furlongs in the denominator and yards
in the numerator, namely "(200 yards)/(1 furlong) and multiply
by that. So far we have:
100 furlong 200 yards
------------ x ------------
1 fortnight 1 furlong
Now to cancel away fortnight in the denominator, create a fraction
which equals 1 that has fortnights in the numerator and days
in the denominator, namely "(1 fortnight)/(14 days) and multiply
by that. So far we have:
100 furlong 200 yards 1 fortnight
------------ x ------------ x -------------
1 fortnight 1 furlong 14 days
Now to cancel away yards in the numerator, create a fraction
which equals 1 that has yards in the denominator and miles
in the numerator, namely "(1 mile)/(1760 yards) and multiply
by that. So far we have:
100 furlong 200 yards 1 fortnight 1 mile
------------ x ------------ x ------------- x -----------
1 fortnight 1 furlong 14 days 1760 yard
Finally to cancel away days in the denominator, create a fraction
which equals 1 that has days in the numerator and hours
in the denominator, namely "(1 day)/(24 hour) and multiply
by that. So we end up with
100 furlong 200 yards 1 fortnight 1 mile 1 day
------------ x ------------ x ------------- x ----------- x ----------
1 fortnight 1 furlong 14 day 1760 yard 24 hour
Now cancel the furlongs:
100 furlong 200 yards 1 fortnight 1 mile 1 day
------------ x ------------ x ------------- x ----------- x ----------
1 fortnight 1 furlong 14 day 1760 yard 24 hour
Now cancel the fortnights:
100 furlong 200 yards 1 fortnight 1 mile 1 day
------------ x ------------ x ------------- x ----------- x ----------
1 fortnight 1 furlong 14 day 1760 yard 24 hour
Now cancel the yards:
100 furlong 200 yards 1 fortnight 1 mile 1 day
------------ x ------------ x ------------- x ----------- x ----------
1 fortnight 1 furlong 14 day 1760 yard 24 hour
Now cancel the days:
100 furlong 200 yards 1 fortnight 1 mile 1 day
------------ x ------------ x ------------- x ----------- x ----------
1 fortnight 1 furlong 14 day 1760 yard 24 hour
Now all you're left with is:
(100)(200)(1)(1 mile)(1)
-------------------------
(1)(1)(14)(1760)(24 hour)
or
(100)(200)(mile)
--------------------
(14)(1760)(24)(hour)
or
20000(mile)
------------
591360(hour)
.0338203463 mi/hr
That may seem awfully slow, but 100 furlongs is only about 11 miles,
and a fortnight is 14 days or 2 weeks, so you'd have to be traveling
at a real snail's pace for it to take you 2 weeks (24 hours a day)
to go only 11 miles!
Edwin
