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)
