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