In a 10 kilometer race, Bill ran 12 kilometer per hour while leo ran 10 kilometers per hour.

How long did it take for them to be 2/3 of a kilometer apart?

speed of Bill = 12km/60 min
speed of Leo = 10m/60 min.
so in 60 minutes the difference in distance travelled by both = 12- 10 = 2 km
so 2 km apart the time is = 60 min.
so 2/3 km apart the time = 60/2*2/3 = 20 minutes ANSWER
PROOF-------------------
in 20 minutes Bill will travel = 12x20/60 = 4 km
in 20 minutes Leo will travel = 10x20/60 =10/3 km
so difference in distance = 4 -10/3 = 2/3 km

40 min