This is a problem about unit conversions. The problem gives yards and seconds, and these need to be turned into miles per hour.
First, convert the yards to miles
440 yards * 3 feet/yard * 1 mile/5280 feet = (440*3)/5280 = 0.25 miles
(Side note: many racing cars are benchmarked by their time in a quartermile drive. You will probably find this distance in the real world of racing a lot)
4.936 seconds * 1 minute/60 seconds * 1 hour/60 minutes = 4.936/3600 hours (I am not doing the division for this as it is a really awkward decimal.)
Now, do miles per hour. Since we are dividing the miles by the hours, invert the hours and multiply by miles.
0.25 * 3600/4.936 = (0.25 * 3600)/4.936 = 900/4.936 = 182.33 miles per hour.
In working this problem, I could have divided the hours fraction and gotten the decimal of 0.001371, and divided 0.25 miles by 0.001371 hours and gotten the same result. But, there would have been more chances for mistakes entering and recording numbers from the calculator.