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An absent minded scientist walks on an escalator at a rate

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An absent minded scientist walks on an escalator at a rate [#permalink] New post 08 Nov 2010, 02:19
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 08:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: an absent minded scientist [#permalink] New post 08 Nov 2010, 02:40
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anilnandyala wrote:
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


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.
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Re: an absent minded scientist [#permalink] New post 08 Nov 2010, 02:54
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.
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Re: an absent minded scientist [#permalink] New post 08 Nov 2010, 07:09
Bunuel wrote:
anilnandyala wrote:
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


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.

Is this a GMAT question.
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Re: an absent minded scientist [#permalink] New post 08 Nov 2010, 08:38
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anilnandyala wrote:
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


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.
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Re: An absent minded scientist walks on an escalator at a rate [#permalink] New post 09 Jul 2013, 08:05
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Re: An absent minded scientist walks on an escalator at a rate [#permalink] New post 05 Aug 2013, 11:16
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?

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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink] New post 01 Sep 2013, 02:34
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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink] New post 02 Sep 2013, 06:24
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
Re: An absent minded scientist walks on an escalator at a rate   [#permalink] 02 Sep 2013, 06:24
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