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1. Darren takes the underground train to work and uses an escalator at the railway station. If Darren runs up 8 steps of the escalator, then it takes him 30.0 seconds to reach the top of the escalator. If he runs up 13 steps of the escalator, then it takes him only 22.5 seconds to reach the top.
How many seconds would it take Darren to reach the top if he did not run up any steps of the escalator at all?
If he runs up 8 steps, then he needs 30.0 seconds to reach the top.
If he runs up 13 steps, then he needs 22.5 seconds to reach the top.
The 5 additional steps take 7.5 seconds.
Therefore, each step takes 1.5 seconds.
Total steps in escalator = 8 + 30.0 / 1.5 = 28 or Total steps in escalator = 13 + 22.5 / 1.5 = 28.
If Darren did not run up any steps at all,
he would reach the top of the escalator in 42.0 seconds (i.e., 28 steps × 1.5 seconds/step).
Alternative Solution through Equations:
Let the total number of steps in the escalator be x.
The escalator moves at a constant speed given by