It takes 1 day to repair 100 meter of road. At this rate how many days will it take to repair 1 kilometer of road?

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

1 km = 1000 m

1/100 = x / 1000 ... 1 day to 100 m = x days to 1000 m

cross multipy

100x = 1000

x = 1000/100

x = 10 days <==