Bobby is going up the escalator. It takes Bobby 80 seconds to walk up the escalator which is moving upwards and 120 seconds to walk up the escalator which is moving downwards. Calculate the time (in secs) taken by Bobby to climb the escalator which is stationary.
Explanation:
Let Bobby's speed be "a" steps per second and escalator's speed be "x" steps per second.
When escalator is moving up, no. of steps N = 80a + 80x (Since Bobby is moving upwards, 80x will be added)
When escalator is moving down, no. of steps N = 120a - 120x (Since Bobby is moving upwards, 120x will be subtracted)
By equating the number of steps, 80a + 80x = 120a - 120x.
⇒ a = 5x
⇒ N = 80a + 80x = 80a + 16a = 96a
∴ Time taken when the escalator is stationary = 96a/a = 96 seconds.
Hence, 96
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