escalator problem...

[psuresh1982]

In an escalator. james runs up 9 step of escalator then he reach the top of the escalator in 42.5 seconds. If he runs up 17 steps then it takes him only 20 seconds to reach the top.

If he didn't run any steps on the escalator at all then howmany second would take him to reach the top?

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suresh

[jamesravid]

I think there is a mistake in ur question....let me prove it...

let us say the escalater moves x steps per second then

9+42.5x = 17 +20x

=> 22.5x = 8
=> x =16/45

No of steps in the escalator is 9 + 85 *16/45 *2
which is not a integer.

nway this is the simplest way to solve this kind of problem

[psuresh1982]

There is no problem in my question....Try to find the answer..I have a solution for this question...

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suresh

[smart_coder]

time required will be 67.8125 secs

[psuresh1982]

sorry smartcoder. That is not a correct answer...

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suresh

[smart_coder]

There r 3 unknowns and 2 equations only!!

[jamesravid]

Is it 245 seconds??

[psuresh1982]

No james. 245 is not a correct answer.

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suresh

[smart_coder]

then wt is correct answer? put ur solution!!

[psuresh1982]

i want to someone will find the answer...So i am waiting today.. If not then i post my answer tomorrow.

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suresh

[vmshenoy]

hi

is it 60 seconds?

[psuresh1982]

No shenoy...60 seconds is not a correct answer.

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suresh

[psuresh1982]

Here is my answer for this question. There are two ways to solve this problem.

First Way of Solution:

Let say x is the total number of steps.

According to my question

(x-9)/42.5 = (x-18) / 20
42.5(x-18) =20(x-9)
42.5x - 765 = 20x - 180
22.5x = 585
x=585/22.5
x=26

Speed of the escalator = (26 - 9 )/42.5 = 0.4

Time to reach the top = Total step/speed = 26/0.4 = 65 seconds.


Second way of Solution:

James using 9 step, took 42.5 sec. to reach top.
James using 18 step, took 20 sec. to reach top.

So 9 additional steps take 22.5 sec.
so each step take 2.5 sec.

So Total step in the escalator = 9 + (42.5 / 2.5) = 26

Time to reach top = 26 * 2.5 = 65 sec.


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suresh

[gripusa]

Sorry suresh , your answer seems wrong to me as if you see , you are using 18 steps second time while in your original post it was 17. Any Way here is my solution;

(x-9)/ 42.5 = (x-17)/ 20

So what you think ?

[smart_coder]

According to your solution :
Steps = 26 but speed of escalator cannot be (26-9) / 42.5 = 0.4
because Escalator always keep moving upwards...So if u r subtracting the number of steps the man climbed i.e 9 from 26, then you should also subtract the time taken by that man in climbing those steps from 42.5 secs
LEt the time taken by that man is t secs for climbing 9 steps
then speed of escalator will be (26 - 9) / (42.5 - t)

[psuresh1982]

ohhhh.....What a foolishness mistake i made...Sorry Sorry friends...

Initially jameravid also point this out..I didn't notice that one...

Once again i say sorry to all of you.

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suresh