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### Math Puzzles & Brain Teasers

Up an Escalator View Puzzle Solve Puzzle
 Hide all answers   View all answers   Print   Try the Quiz 1. Graham takes the underground train to work and uses an escalator at the railway station. If Graham runs up 6 steps of the escalator, then it takes him 77.5 seconds to reach the top of the escalator. If he runs up 13 steps of the escalator, then it takes him only 60.0 seconds to reach the top.How many seconds would it take Graham to reach the top if he did not run up any steps of the escalator at all? Answer: 92.5 Solution: If he runs up 6 steps, then he needs 77.5 seconds to reach the top. If he runs up 13 steps, then he needs 60.0 seconds to reach the top. The 7 additional steps take 17.5 seconds. Therefore, each step takes 2.5 seconds. Total steps in escalator = 6 + 77.5 / 2.5 = 37 or Total steps in escalator = 13 + 60.0 / 2.5 = 37. If Graham did not run up any steps at all, he would reach the top of the escalator in 92.5 seconds (i.e., 37 steps × 2.5 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 Speed of escalator = (x − 6)/77.5 = (x − 13)/60.0 The above equation may be solved as follows. 60.0 (x − 6) = 77.5 (x − 13); or x = (13 × 77.5 − 6 × 60.0) / (77.5 − 60.0) = 37. Now, Speed of escalator = (37 − 6)/77.5 = (37 − 13)/60.0 = 1/2.5 steps/second. Time to reach top = Total Steps / Speed = 92.5 seconds. Food for thought: Does it matter whether the escalator is moving up or down?   Try the Quiz :     Puzzles & Brain Teasers : Up an Escalator 