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Re: an absent minded scientist [#permalink]
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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 walks on an escalator at a rate [#permalink]
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]
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]
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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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


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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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...
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An absent minded scientist walks on an escalator at a rate [#permalink]
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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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mvictor wrote:
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...


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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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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


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
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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Re: An absent minded scientist walks on an escalator at a rate [#permalink]
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