Question

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The distance between two stations A and B is 500 km.Two trains start from two opposite stations sametime on parallel track to cross each other.The speed of the 1st train is 20 km/hr less than that of other train after 3 hours 15 min,the trains are 45 km apart from each other.find the speed of two trains

Answer 1

Assuming distance between A and B is d and speed of train B is s.

After passing each other :

d1(distance travel by A train) = 48 * 12

= 576 km

d 2(distance travel by B train ) = 3* s

d1 + d2 = d

576 + 3*s = d ————————(1)

Before passing assuming both train take t time to pass from starting

d = (s + 48 )* t ———————-(2)

from both equation

s*t + 48*t = 576 + 3*s ——————-(3)

distance travel by train A just after passing = distance travel by train B just before passing

s *t = 576

distance travel by train A before passing = distance travel by train B just after passing

48 * t = 3*s

s = 16*t

from equation (3)

16*t*t + 48*t = 576 + 3 * 16* t

t*t = 576/16

t*t = 36

t = 6 hours

again from (3)

s*6 + 48*6 = 576 + 3* s

3*s = 288

s = 96 km/h

speed of train B is 96 km/h

Answer 2

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Assuming distance between A and B is d and speed of train B is s.

After passing each other :

d1(distance travel by A train) = 48 * 12

= 576 km

d 2(distance travel by B train ) = 3* s

d1 + d2 = d

576 + 3*s = d ————————(1)

Before passing assuming both train take t time to pass from starting

d = (s + 48 )* t ———————-(2)

from both equation

s*t + 48*t = 576 + 3*s ——————-(3)

distance travel by train A just after passing = distance travel by train B just before passing

s *t = 576

distance travel by train A before passing = distance travel by train B just after passing

48 * t = 3*s

s = 16*t

from equation (3)

16*t*t + 48*t = 576 + 3 * 16* t

t*t = 576/16

t*t = 36

t = 6 hours

again from (3)

s*6 + 48*6 = 576 + 3* s

3*s = 288

s = 96 km/h

speed of train B is 96 km/h

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