Well this type of problems isn't exactly my strong suit, but I tried to come up with a solution, so my reasoning is as follows: we know that 1km is 0.621 miles, and the problem incites us to find how much time 1 mile takes, so we need to find how many kms are in a mile:
1km ---> 0.621 miles
<=> 1/0.621=1.610 km ---> 0.621/0.621 = 1 mile
so 1 mile = 1.610 km
Next we need to know how much time 1.610 km takes to run across
We know that:
10 km take 55 mins
and 1.610 = 10/6.211
so we need to divide 55 by the same value
55/6.211 = 8.855 mins
So 10 km ---> 55 mins
1.610 = 10/6.211 km ---> 55/6.211 = 8.855 mins
I hope I didn't mess up.
Hope I helped ^^