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Two sisters ascend 50-step escalators that are moving at the same speed. The older sister can only take 10 steps up the crowded “up” escalator, while the younger sister runs up the empty “down” escalator unimpeded, arriving at the top at the same time as her sister. How many steps does the younger sister take?

Respuesta :

N0seeee

Let the speed of the escalator be x steps per second, and the speed of the younger sister be y steps per second.

Since the older sister can only take 10 steps up the crowded escalator, her net speed is (x - 10) steps per second.

The younger sister is running up the empty escalator, so her net speed is (x + y) steps per second.

The time taken for both sisters to reach the top of the escalator is the same, so we can set up the equation:

50/(x - 10) = 50/(x + y)

Cross multiplying, we get:

50(x + y) =50(x - 10)

50x + 50y = 50x - 500

50y = -500

y = -10

50-10= 40 steps

muzammilbhutia3

Answer:

Since the younger sister runs up the empty "down" escalator unimpeded and arrives at the top at the same time as her sister, the distance she covers must be the same as the older sister's distance, who takes 10 steps.

If both escalators are the same length and the younger sister's escalator is moving down, the number of steps she takes must be the difference between the total number of steps and the steps the older sister takes.

So, the younger sister takes \(50 - 10 = 40\) steps.

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