So,
This is how I mentally do it.
Convert 1 1/3 miles to decimal form.
1 1/3 --> 1.3333333...
Since that is 1/10 of the desired rate, we simply move the decimal place one place to the right.
1.333333... --> 13.3333333...
Convert to fraction form.
13 1/3 mph
Lauren bikes 13 1/3 miles per hour.