When Wallace walks up an escalator at a rate of 1 step per second, he reaches the top after exactly
20 steps. If he hurries and walks up the escalator at a rate of 2 steps per second, he reaches the
top after exactly 32 steps.
How many steps are there on the escalator (excluding of course the ones that aren't visible)?
HINT: Create two equations, one for each climbing speed (1 step per second and 2 steps
per second). In each equation, the number of escalator steps = the number of steps the man has taken + the
number of steps that have moved up automatically from the movement of the escalator. The number of
steps that have moved up automatically in each equation is a function of the speed of the escalator which
is an unknown, but the same variable in each equation.
ANSWER:
80 steps.
EXPLANATION: Let
x represent the number of steps on the escalator and
r represent the rate/speed of the escalator (in steps per second). Now let's set up the
two equations.
Wallace walks up a rate of 1 step per second:
Wallace walks up 20 steps on his own and in the 20s it takes him to walk up those 20 steps, the remaining
steps have been moved up automatically by the movement of the escalator. So: x = 20 steps + 20
seconds × r.
Wallace walks up a rate of 2 steps per second:
Wallace walks up 32 steps on his own and in the 16s it takes him to walk up those 32 steps, the remaining
steps have been moved up automatically by the movement of the escalator. So: x = 32 steps + 16
seconds × r.
Since x is isolated in both equations, the two expressions on the right are equal and we can write:
20 + 20r = 32 + 16r
4r = 12
r = 3 (i.e. the rate/speed of the escalator is 3 steps per second)
Substituting 3 for r in the first equation yields: x = 20 + 60 so there are 80 steps on the escalator.
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
