Nicholas is counting the sheep in a flock as they cross a road. The sheep begin to cross the road at 2:00 p.m. and cross at a constant rate of three sheep per minute. After counting 42 sheep, Nicholas falls asleep. He wakes up an hour and a half later, at which point exactly half of the total flock has crossed the road since 2:00 p.m. How many sheep are there in the entire flock?
(A) 630
(B) 621
(C) 582
(D) 624
(E) 618
Nicholas sleeps for an hour and a half, or 90 minutes.

Since three sleep cross the road per minute, then $3 \times 90=270$ sheep cross while he is asleep. Since 42 sheep crossed before he fell asleep, then $42+270=312$ sleep have crossed the road in total when he wakes up.

Since this is half of the total number of sheep in the flock, then the total number in the flock is $2 \times 312=624$.

ANSWER: (D)

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