537.0 m/s

The path from "meters" to "miles" is 

meters -> centimeters -> inches -> feet -> miles 

The path from seconds to hours is

seconds -> minutes -> hours






Use the conversion 1m = 100cm to create a unit multiplier
to cancel the "m".  Since the "m" is in the numerator,
create the unit multiplier from that conversion that has
"m" in the denominator so that it will cancel with the
"m" in the numerator and bring in "cm" in the numerator.
So create the unit multiplier 




Use the conversion 60s = 1min to create a unit multiplier
to cancel the "s".  Since the "s" is in the denominator,
create the unit multiplier from that conversion that has
"s" in the numerator so that it will cancel with the
"s" in the denominator and bring in "min" in the numerator.
So create the unit multiplier 



Use the conversion 1in = 2.54cm to create a unit multiplier
to cancel the "cm".  Since the "cm" is in the numerator,
create the unit multiplier from that conversion that has
"cm" in the denominator so that it will cancel with the
"cm" in the numerator and bring in "in" in the numerator.
So create the unit multiplier 



Use the conversion 1hr = 60min to create a unit multiplier
to cancel the "min".  Since the "min" is in the denominator,
create the unit multiplier from that conversion that has
"min" in the numerator so that it will cancel with the
"min" in the denominator and bring in "hr" in the numerator.
So create the unit multiplier 



Use the conversion 1ft = 12in to create a unit multiplier
to cancel the "in".  Since the "in" is in the numerator,
create the unit multiplier from that conversion that has
"in" in the denominator so that it will cancel with the
"in" in the numerator and bring in "ft" in the numerator.
So create the unit multiplier 



Use the conversion 1mile = 5280ft to create a unit multiplier
to cancel the "ft".  Since the "ft" is in the numerator,
create the unit multiplier from that conversion that has
"ft" in the denominator so that it will cancel with the
"ft" in the numerator and bring in "mile" in the numerator.
So create the unit multiplier 



Now cancel the meters:

  

Now cancel the seconds:



Now cancel the centimeters:



Now cancel the minutes:



Now cancel the inches:



Now cancel the feet:



So you are left with this (ignoring the 1's):

 = 1178.9 miles per hour.

Edwin