SOLVING ESCALATOR PROBLEMS IN TIME DISTANCE SPEED

Problem 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.

Problem 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.

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