A man standing on a 170 metre long platform watches that

A man standing on a 170 metre long platform watches that a train takes
7 1 seconds to pass him and 21 seconds to cross
2
the platform. Find the speed of train.

Let the length of the train be x m and its speed y m/sec.
Distance covered in crossing the platform = 170 + x metres
and time taken = 21 seconds

∴ Speed y =	170 + x	...(i)
	21

Distance covered to cross the man = x metres
and time taken = 7

and time taken = 7	1	=	15	seconds
	2		2

∴ Speed y =	x	=	2x	...(ii)
	15/2		15

From equations (i) and (ii),

170 + x	=	2x
21	=	15

⇒ 2550 + 15x = 42x
⇒ 42x – 15x = 2550
⇒ 27x = 2550

⇒ x =	2550	= 94	4	metres
	27		9

From equation (ii),

y =	2 × 2550
	15 × 27

=	340	= 12	16	m per sec.
	27		27

Hence, speed = 12	16	m per sec.
	27