train problem

[mahesh_mak19]

two persons are travelling opposite on a railway track,a train passes first person in same direction in 20 secs and aftercrossing the train had travelled for 10 min and then crosses the second person opposite to it in 18 secs ,after the train had crossed him then at what time will they meet?

this is given in infosys plz send me the solution to my mail mahesh_mak19@yahoo.co.in

[WISDOM]

lemme try this! indeed a very good problem. how didu do in infosys or do u still have to appear in it?

let speed of person 1 = s1 m/s

speed of person2 = s2 m/s

speed oftrain =s m/s

and let distance between the s1 and s2 = x m at t=0 and at t=0, the train starts from x=0 position and at the same time s1 and s2 starts moving.

for person 2:

in 20 seconds that the train takes to overtake person 1, person 2 moves 20* s2 metres

in same 20 seconds, train moves 20s metres towards second person

further, train meets seconds person after 10 min = 600sec

so in that time both move 600*s2 and 600*s metres

so, 20(s+s2) + 600(s+s2) = x

or 620(s+s2) = x ...........................(1)

I length of train = L metre

then L/(s-s1) = 20 & L/(s+s2) = 18

=> s = 10s1 + 9s2.........................(2)

For person 1 and person, they will meet when both of them have covered the distance of x metre measured from instant t=0

in 20 seconds, they travelled 20(s1+s2)

in further 10 minutes, they travelled 600*(s1+s2)

let they meet after n sec after train 2 meets second person

so x = 620(s1+s2) + n(s1+s2)............................(3)

from (1)&(3)

(620+n)(s1+s2) = 620(s+s2)..........(4)

further s+s2 = 10s1+9s2+ s2 = 10(s1+s2)...........using (2)

put it in (4)

(620+n)(s1+s2) = 620*10*(s1+s2)

=> n = 6200-620 = 5580 sec after 2nd train meets person 2

or (5580-18) sec after 2nd train crooses the second person

= 5562 seconds = .......min, hr

i hope i have done my best in explaining this. if i have messed up anywhere which is very likely, then do tell me. further, i am sure by now u must have solved this question as it is alreadymore than 1 month since u asked this question. So, i wud like to know u'r method

by far, the best question on this site and a difficult one two as we normally ignore the speeds of person in comparison to train etc but here it wud make a difference!