Problem: An escalator (moving staircase) of uniform steps visible at all times descends at constant speed. Two boys, and , walk down the escalator steadily as it moves, negotiating twice as many escalator steps per minute as . reaches the bottom after taking steps while reaches the bottom after taking steps. Then is:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the time needed for a full step, at any given level of the escalator, to reach the next level, be designated as unit time. Then 's time to travel the escalator may be represented as where is the number of escalator steps covered by in unit time. Similarly A's time may be represented as .
Since the rates of and are inversely proportional to their negotiated number of steps, so that . Setting , we have . Alternatively, we set and obtain .