Oof! An hour!? Dimensional analysis can be really tricky, but let's see what we can do...
First of all, it will be important to have some conversion factors:
1 km = 0.621 miles
Starting with part A, let's write down our given number as a fraction, including UNITS:
(1227.99 km / 1 hr)
(on your paper at home, please put the 1227.99 km ABOVE 1 hr, but for simplicity's sake, I'm using "/" )
For our conversion factor, we can write this number as:
(1 km / 0.621 miles) or we can write it as: (0.621 miles / 1 km), we can do this, because this number is essentially (1 thing / 1 other thing). The value isn't changing, but the UNITS are changing.
Now, on the far right side, write "=" then the desired units:
(1227.99 km / 1 hr) = ??? miles / hr
So, to cancel out km (ON BOTTOM), and have miles ON TOP, should you multiply by (0.621 miles / 1 km) or should you multiply by (1 km / 0.621 miles)?
We should use (0.621 miles / 1 km) because we want miles ON TOP:
so (1227.99 km / 1 hr) * (0.621 miles / 1 km) = (1227.99 * 0.621) km ÷ hr * miles ÷ km
= 762. 58 km ÷ hr * miles ÷ km
= 762. 58 miles ÷ hr
= 762. 58 miles/hr which is part A!
Now, given that:
1 mile = 5280 ft
1 hr = 60 min
1 min = 60 sec
We now have the fractions:
(1 mile / 5280 ft)
(1 hr / 60 min)
(1 min / 60 sec)
And all of these are just 1/1 (so if we multiply or divide, we're not changing the VALUE of our original number, only the UNITS on that number).
Once again, write the starting number (this time using the answer from part A) on the left, and the desired units on the far right:
762. 58 miles / 1 hr = ??? ft / sec
This time, we want to cancel out miles, and put ft ON TOP:
(762.58 miles / 1 hr) * (5280 ft / 1 mile) = ??? ft / sec
But now we want sec on the BOTTOM, so we'll write the conversion fraction with SEC on the BOTTOM in somewhere towards the middle (leaving space):
(762.58 miles / 1 hr) * (5280 ft / 1 mile)* * (1 min / 60 sec) = ??? ft / sec
This leaves a space for one more conversion factor...and it needs to cancel out both the hours and the minutes...i.e. minutes are on top right now, but we need them to be ON BOTTOM, and hrs are on bottom right now, but we need them to be ON TOP, so will you use (1 hr / 60 min) or (60 min / 1 hr)?
To cancel all of the units out, (1 hr / 60 min) should be used:
(762.58 miles / 1 hr) * (5280 ft / 1 mile) * (1 hr / 60 min) * (1 min / 60 sec) = ??? ft / sec
= (762.58 * 5280 ÷ 60 ÷ 60) miles ÷ hr * ft ÷ mile * hr ÷ min * min ÷ sec
= 1118.45 miles ÷ hr * ft ÷ mile * hr ÷ min * min ÷ sec
= 1118.45 ÷ hr * ft * hr ÷ min * min ÷ sec
= 1118.45 * ft ÷ min * min ÷ sec
= 1118.45 ft ÷ sec
= 1118.45 ft / sec
