Two boys enter a running escalator on the ground floor in a shopping mall and they do some fun on it. The first boy repeatedly follows $p_{1} = 1$ step up and then $q_{1} = 2$ steps down whereas the second boy repeatedly follows $p_{2} = 2$ steps up and then $q_{2} = 1$ step down. Both of them move relative to escalator with speed $v_{r} = 50 c m s^{- 1}$ . If the first boy takes $t_{1} = 250 s$ and the second boy takes $t_{2} = 50 s$ to reach the first floor, how fast is the escalator running?

Open in App

Solution

Let speed of escalator be v

Displacement of boys is come i.e, from ground floor to first floor.

We know, displacement $= s p e e d \times t i m e$

First boy more one step down everytime & takes more time. So,

$(50 - V) 250 = (50 + V) 50 \Rightarrow V = \frac{50}{2} c m / s V = 25 c m / s$

Suggest Corrections

Similar questions

Q. A boy while walking takes 23 steps in 15 seconds to come down by an escalator that is coming down. Find the total number of steps in the escalator, if the same boy takes 31 steps in 10 seconds to come down while running, on the same escalator that is coming in the downward direction.

Q. On a linear escalator running between two points A and B, a boy takes time

t_{1}

to move from A to B, if the boy runs with a constant speed on the escalator. If the boy runs from B to A, he takes time

t_{2}

to reach B from A. What is the time taken by the boy to move from A to B if he stands still on the escalator?

[The escalator moves from A to B]

Q. A boy takes

90

second to walk up a stalled escalator. However, if the escalator is moving and he stands on the escalator, he is carried up in one minute. how much time the boy would take to walk up the moving escalator?

Q. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time

t_{1}

. If he remains stationary on a moving escalator, then the escalator takes him up in time

t_{2}

. The time taken by him to walk up on the moving escalator will be:

An escalator is moving up at a speed of 1 step per 2 seconds. A person is also moving up on that escalator. He started to walk at the rate of 2 steps per second. He reached the top of the escalator in 10 seconds. How many steps are there in that escalator?

Join BYJU'S Learning Program

Let speed of escalator be v Displacement of boys is come i.e, from ground floor to first floor. We know, displacement =speed×time First boy more one step down everytime & takes more time. So, (50−V)250=(50+V)50⇒V=502cm/sV=25cm/s

Let speed of escalator be v

Displacement of boys is come i.e, from ground floor to first floor.

We know, displacement $= s p e e d \times t i m e$

First boy more one step down everytime & takes more time. So,

$(50 - V) 250 = (50 + V) 50 \Rightarrow V = \frac{50}{2} c m / s V = 25 c m / s$