## SOLVING ESCALATOR PROBLEMS IN TIME DISTANCE AND SPEED

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.

## Related topics

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.

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6