Question

Two men are going along a track of rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec. After the train has passed, when the two persons will meet?

Answer 1

Let us consider that speed of train , first man and second man are respectively t, f and s.

According to first given condition goods train crossed the first person moving in same direction in 20 sec.

so length of the will be 20(t-f)

similarly train crossed the second man in 18 sec.

so length of the train will be 18(t+s)

on comparing these two equations, we get 20(t-f) = 18(t+s)

or 2t = 20f + 18s

or t = 10f + 9s

now it is given that After 10 min the train crossed the other person who is coming in opposite direction so

if we consider this way of train as L then the next equation will be

L = 600t (here 600 is used for 10 minutes)

finally as asked in the question the time required to meet the two man after the train has passed will be given by

time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes}

= (600t-600f)/(f+s)

= [600(10f+9s)-600f]/(f+s)

= 600(10f+9s-f)/(f+s) = 600*9(f+s)/(f+s) = 600*9 seconds = 600*9/60 min

= 90 minutes