This is a simple proportion problem. Assuming that the rate is constant for how fast the person can repair the road, the number of days it takes to repair the road will be exactly 10 days.
1 day to repair 100 meters ? days to repair 1 kilometer
1 kilometer = 1000 meters Substitute 1000 meters for 1 kilometer
So set up your proportion as so: 1 day/ 100 meters = x / 1 kilometer 1 day / 100 meters = x/ 1000 meters
x = 10 days