The formula with 1.67 substituted
miles = 1.67 ÷ 1.609344 = 1.038
The constant is an exact definition, not a rounded factor: the mile is 1.609344 km, the US gallon is 3.785411784 litres and the imperial gallon is 4.54609 litres. The Kilometres to Miles Converter explains where each comes from and gives a longer table.
At a walking pace of 5 km/h, 1.67 km takes about 20 minutes. At an easy running pace of 10 km/h it takes about 10. In metres it is 1,670.
What 1.67 kilometres means in practice
1.67 km is looked up because it is what a GPS watch reports for a route that was meant to be a mile: a mile is 1.609 km, and the extra 60 metres is the detour round a parked van or the loop back to the front door. It is 1.04 miles, close enough that most runners log it as one.