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Escalator

Math Puzzle:

You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator. How many steps do you need if the escalator stands still?

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Solution:

100 Steps.

Let v be the speed of the escalator, in steps per second. Let L be the number of steps that you need to take when the escalator stands still. Upwards (along with the escalator), you walk 1 step per second. You need 50 steps, so that takes 50 seconds. This gives: L - 50 × v = 50. Downwards (against the direction of the escalator), you walk 5 steps per second. You need 125 steps, so that takes 25 seconds. This gives: L + 25 × v = 125. From the two equations follows: L = 100, v = 1. When the escalator stands still, you need 100 steps.

6 comments:

pg... said...

100 steps

pg... said...

say escalator speed x steps/sec.

so total steps = 50+50x.(from upward condition).
Total time to reach up is 50 sec.
total time to reach down = 25 sec.(125 steps, 5 steps/sec)
total steps = 125- 25x
50+50x = 125 - 25x
75 x = 75=>x =1,
so total steps = 50 + 50*1= 100

class vii a said...

thnx for this answer can anyobody tell me
How many right angled triangles with integral sides hav one side 15

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