Solution: Let the speed of boys be 2, then the speed of girls is 1.
∵ Boys go to Grade 27 and girls go to Grade 18.
∴ The time for boys is 27÷2= 13.5, and that for girls is 18÷ 1= 18.
Assuming that the escalator runs X-class during boys' walking time, then the escalator runs X-class during girls' walking time.
The formula can be: 27+x= 18+(4/3)x,
Solution: x=27,
So the escalator has 27+27=54 steps.
Boys walk twice as fast as girls every minute,
It shows that the time ratio for boys to reach the top from grade 27 and for girls from grade 18 is 27/2:18 = 3: 4;
The relative speed ratio is 1/3: 1/4=4:3.
If the relative speed of boys is 4x, the relative speed of girls is 3x and the elevator speed is v,
According to the fact that boys walk twice as many steps per minute as girls, we know that:
(4x-v)/(3x-v)= 2/ 1 = & gt； 4x-v=6x-2v = >2x=v
The elevator speed is half of the boy's relative speed and equal to the boy's absolute speed;
So the outer part of the elevator is 54 floors;
Let's set up X-class for women, 2x-class for men, Y-class for escalators and N-class for the outside of escalators.
(n-27)/y=27/(2x)，
(n- 18)/y= 18/x，
The solution is n=54.
(2) It takes 54/(4x) minutes for boys to get on the elevator, 27/x minutes for boys to get down the stairs and 40.5/x minutes for boys to get down the stairs.
It takes a girl 18/x minutes to get on the elevator, 54/x minutes to get off the stairs and 72/x minutes to get up.
After 8 1 minute, the boys walked 2 laps and the girls walked 1+ 8/72 laps.
After 99 minutes, the boy walked 2+0.5+(99-81-13.5)/27 = 2.5+1/6.
The girl walked1+0.5+(99-72-18)/54 =1.5+1/6 laps.
At this time, the boys caught up with the girls for the first time, and the boys passed 3 * 27+(2+1/6) * 54 =198 steps.