An escalator moves at a constant rate from one floor up to the next floor. Jack walks up 29 steps while travelling on the escalator between the floors. Jill takes twice as long to travel between the floors and walks up only 11 steps. When it is stopped, how many steps does the escalator have between the two floors?
(A) 47
(B) 51
(C) 40
(D) 36
(E) 69
Solution 1

Suppose that the escalator was two floors long, instead of just one, and that Jack and Jill start walking at the same time. Then Jack will reach the second floor at the same time Jill reaches the first floor (since it takes Jill twice as long to climb one floor). In that time, Jack will have climbed 2(29) steps and Jill will have climbed 11 steps, so there will be $47=2(29)-11$ steps between them on the escalator.

These 47 steps represents the distance between two floors, or the length of the escalator.

## Solution 2

Suppose that $N$ is the total number of steps on the elevator.

As Jack walks up the escalator, he walks 29 steps, so he is carried $N-29$ steps by the escalator.

As Jill walks up the escalator, she walks 11 steps, so is carried $N-11$ steps by the escalator.

Since Jill's trip takes twice as long as Jack's trip, then she must be carried up twice the number of steps that Jack is carried, ie.

$$
\begin{aligned}
N-11 & =2(N-29) \\
N-11 & =2 N-58 \\
N & =47
\end{aligned}
$$

Therefore, the number of steps is 47 .

ANSWER: (A)

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