Walking up the escalator

• steps total = steps by self + steps due to elevator
• steps due to elevator = constant rate of elevator * time spent going up stairs
• Let us make some easy numbers to visualize this:
• Person a: Rate = 1 step/s, Time spent climbing = 27 seconds (since he walked up 27 steps before reaching top)
• Person b: Rate = .5 step/s, Time spent climbing = 36 seconds (since he walked up 18 steps before reaching top)
• Both people climbed n steps. The escalator did (n-27) steps for person A and (n-18) steps for person B.
• number of steps / time = rate of escalator = constant value for both people

Person a's rate of escalator = Person b's rate of escalator

(n-27)/27 = (n-18)/36

n = 54 steps

Let the escalator speed be $e$ , $t_1$ the time for Aaron to go up, and $t_2$ the time for Baron to go up. Then we have the equation: $27 + e*t_1=18+e*t_2$ . So $9=e*t_2(1-\frac{t_1}{t_2})$ . We also know that Aaron's speed is twice of Baron's speed, so $\frac{27}{t_1}=2*\frac{18}{t_2}$ , therefore $\frac{t_1}{t_2}=\frac{3}{4}$ . And we get $e*t_2=36$ , the total number of steps is then $18+36=54$ .

Let Va, Vb, V be the velocity of a, b, and elevator. But Va = 2Vb.
Ta, time to move 27 steps by a, Tb for 18 by b.
Time = distance X velocity. Ta = 27/(2Vb) , Tb = 18/Vb
n = Time * actual velocity. n = Ta ( 2Vb + V ) also n = Tb ( Vb + V ) gives
{27/(2Vb)} (2V + V ) = {18/Vb} {Vb = V ) gives 2Vb = V = Va
Thus velocity of b and elevator is same thus elevator also moves 27 steps with b.

THUS TOTAL STEPS = 27 + 27 = 54.

simple logic guys...no hardcore mathematics!! i just started assuming numbers for n...strarted assuming with 36...45..and went on to 54...and satisfied...! see...if there are 54 steps...and 27 he aaron walked..it means 27 steps are gone by the speed of the escalator...it means..aaron's speed is 1 step walked as 1 step goes...now...baron's speed is half of it...soo..baron walks half step as 1 step goes ....which eventually ends up on 18 plus 36+ 54..! i know this method's gonna get a lot of BOO's...but it's my assumption method like everytime...:D!

let :v be Aaron's speed... t be time taken by Aaron to reach level 2... t' be time taken by baron to reach level 2... r be the number of steps moved by the escalator per unit of time... Aaron moved 27 steps during t instead of n, due to the escalator. hence, the ecalator moved (n-27) during t. so, r=((n-27)/t). Baron moved 18 steps during t' instead of n, due to the escalator. hence, the ecalator moved (n-18) during t'. so, r=((n-18)/t'). now, we will search for a relation between t and t'. we know: time=(steps/rate). so, t=27/v and t'=18/(v/2). using these two equations, we get t'=(4/3)t. substituting this in r=((n-18)/t'), and setting r=r, we will find n.

the solutions is Aarons walks up 27 and Baron takes 18 steps to do that this the solution is 27+27 coz Aarons speed is twice Barons Speed Regards ZAIN KHAN