Question

A cheetah ran 300 feet in 2.92 seconds . What was the cheetah's average speed in miles per hour ? Show your work .

Answer 1

You have the Cheetah's speed ... it's  (300/2.92)  feet/second .
Now you need to change the units of that fraction to mile/hour.

You can change the numerator, then change the denominator
and put it back together.  To me, that's too many chances to
make a mistake.  I prefer to think of it this way:

Make fractions of helpful unit conversions, like

           (1 mile / 5,280 feet)  and  (3,600 sec/hour) .

In each of these, the numerator and denominator are equal,
so the fraction is equal to ' 1 ', and you can multiply other things
by it without changing the value of the other thing.  That's exactly
what you need.
Watch this:

       (300 ft / 2.92 sec) x (1 mile / 5,280 feet) x (3,600 sec/ 1 hour)

   =  (300 x 1 x 3,600) / (2.92 x 5,280 x 1) (ft-mile-sec/sec-ft-hr)

Look at the units on the end: The 'ft' and 'sec' each appear in the
numerator and denominator, so they can be canceled out, and
you're left with 'mile/hour'.  This gives you a nice check at this
stage that your work so far is correct.  If you had flipped one
of the unit conversions upside down by mistake, then the units 
would be screwy at this point, and you'd know right now to go
back and look for a mistake.

But the units are good, so all you have to do now is stuff the
numbers through your calculator:

     (300 x 1 x 3,600) / (2.92 x 5,280 x 1) (ft-mile-sec/sec-ft-hr)

 =  (1,080,000 / 15,417.6)  mile/hour

 =        70.05  mile/hour

Answer 2

Cheetah ran 300 feet in 2.92 seconds.

Average speed in miles per hour.

Converting 300 feet to mile.
5280 feet  =  1 mile
1 feet    =    (1/5280) mile
300 feet =    (1/5280) * 300 = (300/5280) = (30/528) = (10/176) mile.

2.92 seconds to hour.
3600 seconds  =    1 hour
1 second          =  (1/3600) hour
2.92 seconds    =    2.92 * (1/3600) =  (2.92/3600) hour.

Speed of Cheetah in miles per hour =    (10/176) mile  /  (2.92/3600) hour
                                                     =  70.05 miles/hour