**Solving Escalator Problems in Time Distance and Speed :**

In this section, we will learn how to solve escalator problems in the topic time distance and speed.

**Example 1 :**

Frank and Ronnie embarked on a moving escalator to the second floor of a shopping mall. Frank walked up the escalator at a speed of 2 steps every second. At the same time, Ronnie walked up the same escalator at a speed of 3 steps every 2 seconds. Frank arrived at the second floor in 25 seconds. If took Ronnie 30 seconds to reach the same floor. How many steps had the escalator when it was stationary ?

**Solution :**

Escalator is a moving object, it is also having a speed.

So, the distance traveled by the man in escalator = sum of distances of both escalator and a man.

Let x be the number of steps traveled by the escalator per second.

Distance = Time ⋅ Speed

**Frank :**

He is walking at the speed of 2 steps every second.

Time taken to reach the second floor is 25 seconds.

**Ronnie :**

He is walking at the speed of 3 steps every 2 seconds.

So, he is walking 3/2 steps in 1 second.

Time taken to reach the second floor is 30 seconds.

Distance traveled by Frank = 25(2) + 25x

= 50 + 25x--------(1)

Distance traveled by Ronnie = 30(3/2) + 30x

= 45 + 30x --------(2)

(1) = (2)

50 + 25x = 45 + 30x

5 = 5x

x = 1

So, escalator is moving 1 step per second.

By applying the value of x in (1), we get

= 50 + 25 (1)

= 75

Hence the escalator is having 75 steps when it was at stationary.

**Example 2 :**

Henry and Robert embarked on a moving escalator. Impatient with the speed of escalator. Henry walked at a speed of 3 steps per second while Robert walked at a speed of 2 steps per second. How many steps had the escalator when it was stationary ? It was given Henry took 20 seconds to arrive at the second floor and Robert took 25 seconds to arrive at the same floor.

**Solution :**

Let x be the number of steps traveled by the escalator per second.

Distance = Time ⋅ Speed

**Henry :**

He is walking at the speed of 3 steps per second.

Time taken to reach the second floor is 20 seconds.

**Robert :**

He is walking at the speed of 2 steps per second.

Time taken to reach the second floor is 25 seconds.

Distance traveled by Henry = 20(3) + 20x

= 60 + 20x--------(1)

Distance traveled by Robert = 25(2) + 25x

= 50 + 25x --------(2)

(1) = (2)

60 + 20x = 50 + 25x

10 = 5x

x = 2

So, escalator is moving 2 steps per second.

By applying the value of x in (1), we get

= 60 + 20 (2)

= 100

Hence the escalator is having 100 steps when it was at stationary.

- Find the time taken by the train to pass a man
- Find the time taken by a train to pass a bridge or tunnel
- Train passes a moving object in the same direction
- Problems on finding the length of the train
- Finding the average speed of the round trip
- Finding the speed when the distance traveled is same

After having gone through the stuff given above, we hope that the students would have understood how to find the time taken by a train to pass a man.

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