A boat covers 12 km upstream and 18 km downstream in 3 hours,

A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers
36 km upstream and 24 km downstream in 6 1 hrs
2
. What is the speed of the current ?

Let the speed of boat in still water be p kmph and that of current be q kmph, then
According to question ,

12	+	18	= 3........(i)
p - q		p + q

36	+	24	=	13
p - q	+	p + q	=	2

By equation (i) × 3 – equation (ii),

54	-	24	= 9 -	13
p + q	-	p + q	= 9 -	2

⇒	30	=	5	⇒ p + q = 12 .........(iii)
	p + q		2

From equation (i),

⇒	12	+	18	= 3
	p - q		12

⇒	12	= 3 -	3	=	3
	p - q		2		2

⇒ p - q =	12 × 2	= 8........(iii)
	3

∴ Speed of current =	1	(12 - 8) = 2 kmph
	2