Speed P6

Alice is going up an escalator. When she takes 2 steps per second, she reaches the top in 24 steps. When she takes 1 step per second, she reaches the top in 16 steps. How long will she take to reach the top if she just stands on the escalator?


      2 steps                SE steps
   per second          per second
     24 steps
|-------------------|------------------|

2 steps --> 1 s
24 steps --> 24/2 = 12 s


       1 step                  SE steps
    per second           per second
       16 steps
|-----------------------|--------------|

1 step --> 1 s
16 steps --> 16 s


24 + 12 SE --> 16 + 16 SE
4 SE --> 24 - 16 = 8
SE --> 8/4 = 2 steps per second

24 + 2 x 12 = 48 steps  [or 16 + 2 x 16 = 48 steps]

48 / 2 = 24 s

She took 24 seconds.