Since in about 675 revolutions of the wheel, Songhee travels one mile, then in about:
[tex]675\times10\text{ revolutions}[/tex]Songhee travels 10 miles.
Then:
[tex]10\text{mi}\leftrightarrow6750\text{ revolutions.}[/tex]Now, we know that Songhee rides her bicycle at 10 miles per hour, substituting 10mi=6750revolutions we get that Songhee rides her bicycle at:
[tex]6750\text{revolutions per hour.}[/tex]Answer: 6750 revolutions per hour.