Since time is obtained by dividing distance and speed, then Skye took 3 km/150 km per hr. = 1/50 of an hour to finish the first 3 kilometers of the race.
His speed on the next 2 kilometers was 150 + 50 = <<150+50=200>>200 kilometers per hour.
Hence, it took him 2 km/200 km per hr. = 1/100 of an hour to finish the next 2 kilometers.
His speed on the remaining 1 kilometer is 150 x 2 = <<150*2=300>>300 kilometers per hour.
Hence, it took him 1/300 of an hour to finish the 1 kilometer.
So, the total time it took for Skye to complete the race was 1/50 + 1/100 + 1/300 = 1/30 of an hour.
Therefore, his average speed for the entire race was 6 km/ 1/30 hour = 180 kilometers per hour.
#### 180