An absent minded scientist walks on an escalator at a rate

Question

An absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds. While coming back, walking at the same speed he reaches the starting point in 45 seconds. What is the number of steps on the escalator?

A. 60
B. 90
C. 105
D. 120
E. 140

A. 60
B. 90
C. 105
D. 120
E. 140

Bunuel · Accepted Answer

Let the rate of the escalator be  x  steps per second and the length of the escalator  y  steps.

Then  \frac{y}{x+4}=15  and  \frac{y}{4-x}=45  --> solving for  y  -->  y=90 .

Answer: B.

KarishmaB · Answer

Escalator questions tend to confuse people but the point to note here is that they are just like Boats and Streams questions. If you are going in the direction of the escalator, it is like going downstream and your effective speed will be your speed + escalator speed. When you are going against the escalator, it is like going upstream and your effective speed will be your speed - escalator speed. The total distance to be traveled is the total number of steps on the escalator. 
Then, you can very easily make the equations made by Bunuel and Sarang above:
 \frac{y}{x+4}=15 and \frac{y}{4-x}=45

You can take a couple of quick guesses to solve this and in most cases you will get your answer in a couple of guesses.
e.g. lets say if x = 1, y = 75 from 1st equation
but x = 1 gives y = 135 in 2nd equation. So x is not 1
If x = 2, y = 90, from 1st equation
x = 2 gives y = 90 in 2nd equation. So x = 2 and y = 90.
Fun fact about GMAT: They give you numbers that make your life easy but twist concepts to make you think.

Also, if I am not wrong, these are CAT questions. I have not seen such questions in OG/Test prep material that I have come across. Nevertheless, every question is good for practice if you have the time. If time is less, you would do better to focus on 'GMAT type' questions available in OG.

Sarang · Answer

Scientist is absent minded. He uses same escalator while walking in both directions

Let S be speed of escalator

Case1-->same direction as that of escalator, so D/(4+S)= 15
Case2-->against direction of escalator, so D/(4-S) = 45
Combining above 2 equations- 15(4+S)= 45(4-S), S=2

Therefore number of stairs= 90. Answer: B.

WholeLottaLove · Answer

An absent minded scientist walks on an escalator at a rate of 4 steps per second and reaches the other end in 15 seconds. While coming back, walking at the same speed he reaches the starting point in 45 seconds. What is the number of steps on the escalator?

A. 60
B. 90
C. 105
D. 120
E. 140

It took me a while to figure out why the fact that the scientist was "absent minded" was relevant. He walked on the escalator the right way then went in the opposite direction against the direction it was moving in!

We are given time and rate for both directions. We have to realize that because the escalator is moving, that adds (or subtracts) from his forward momentum.

time = distance/speed
t1: 15 = d/(r+4)
15r+60 = d

t2: 45 = d/(4-r)  The scientist moves at the same speed but because he is going against the motion of the escalator his forward movement is slowed down. Therefore, we subtract the escalators rate from his rate of 4 steps/second. 
180-45r = d

15r+60 = 180-45r
60r - 120
r=2

15 = d/(r+4)
15 = d(2+4)
15 = d(6)
90 = d

ANSWER: B. 90

agourav · Answer

T = total no. of steps in escalator
n = speed of escalator in steps per second
4 = steps per sec of the scientist

(n+4)=T/15 and (4-n) = T/45
=> n = 2
=> T = 90

1980ajaykumar · Answer

As we can see, ratio of time take when going with the escalator to time taken against the escalator is 3

Also it is understandable that, speed of the escalator must be less then the speed of the scientist ( as the scientist is able to come down while moving against the escalator )

Futher is we assume X (steps/sec) be the avg. speed of the escalator then

(4+X)/(4-X) = 3
 i.e. X=2

Hence no of steps = (4+X)*15 = (4-X)*45 = 90

Lucky2783 · Answer

time taken going up 45sec
time taken going down 15sec
it tells going down speed is 3times the speed going up.
4+E=3(4-E)
E=2
in 15secs scientist will move 60 steps
in 15secs escalator will move 2×15=30 steps
answer 90

mvictor · Answer

to be honest..I did not even know how to approach this question...
4*15 = 60 steps
4*45 = 180 steps
he makes 120 steps more in 30 additional seconds.
if he skipped every other step while going up - he would have walked 90 steps
if he walked 2 times backwards the same steps, then he walked 180.

that's the only way i got to 90..but don't understand how it works in practice...

gracie · Answer

let r=rate of escalator
(4+r)(15)=(4-r)(45)
r=2 steps per second
(4+2)(15)=(4-2)(45)=90 steps on escalator

KarishmaB · Answer

If you want to approach it this way, here is how to get it:

Scientist takes 4*15 steps while going in the direction of the escalator. He is taking 60 steps and the escalator is taking some additional steps for him.
He takes 4*45 = 180 steps while going against the direction of the escalator. He is taking 180 steps because the escalator is cancelling out some of his steps. 
The difference in these two numbers is 180 - 60 = 120. This 120 is the sum of the number of steps the escalator adds and cancels out.

The escalator's speed is constant. It makes the same number of steps every second. So in 45 secs, it will make 3 times the number of steps that it does in 15 secs. So if it makes s steps in 15 secs (add s steps to the scientist), it will make 3s steps in 45 secs (will cancel out 3s steps of the scientist).

s + 3s = 120
s = 30

So total steps of the escalator are 60 + 30 = 90
or total steps of the escalator = 180 - 3*30 = 90

JeffTargetTestPrep · Answer

We can assume the speed of the escalator is x steps per second. Thus, when he goes along with the direction of the escalator, the combined speed is 4 + x. Since we know it takes 15 seconds to reach the other end, the escalator must be 15(4 + x) steps. 
 
While coming back, he goes against the direction of the escalator. Thus the net speed is 4 - x. Since we know it takes 45 seconds to reach the starting point, the escalator must be 45(4 - x) steps.
 
Since the escalator must have the same number of steps regardless which way he goes, we have:
 
15(4 + x) = 45(4 - x)
 
4 + x = 3(4 - x)
 
4 + x = 12 - 3x
 
4x = 8
 
x = 2 
 
Thus, the escalator has 15(4 + 2) = 15(6) = 90 steps.
 
Answer: B

himanshusb09 · Answer

If I solve it like...

(S+4)*15 = (S-4)*45
=> (S+4) = (S-4)*3
=> S+4 = 3S - 12
=> 16 = 2S
=> S=8

=> Distance i.e. Number of steps = (8+4)*15 = 180

Assumption is... scientist's speed is greater than that of escalator. What's wrong in this?

An absent minded scientist walks on an escalator at a rate

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