A man rows a boat downstream for 3 hours and then upstream for 3 hours. If he covered a total distance of 12km, find the speed of the water current.


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Question Number 30538 by SammyKT last updated on 23/Feb/18

$A m a n r o w s a b o a t d o w n s t r e a m$ $f o r 3 h o u r s a n d t h e n u p s t r e a m$ $f o r 3 h o u r s . I f h e c o v e r e d a$ $t o t a l d i s t a n c e o f 12 k m, f i n d$ $t h e s p e e d o f t h e w a t e r c u r r e n t .$
	Answered by mrW2 last updated on 24/Feb/18

	$i f t h e w a t e r w e r e s t i l l, t h e m a n w o u l d$ $c o m e b a c k t o h i s s t a r t i n g p o i n t a f t e r$ $6 h o u r s . t h a t m e a n s t h e w a t e r m o v e s$ $h i m 12 k m i n 6 h o u r s . t h e s p e e d o f$ $w a t e r i s h e n c e 12 / 6 = 2 k m / h .$
	Commented by mrW2 last updated on 25/Feb/18

	$3 \times (v_{m} + v_{w}) - 3 \times (v_{m} - v_{w}) = 12$ $\Rightarrow 6 \times v_{w} = 12$ $\Rightarrow v_{w} = \frac{12}{6} = 2 k m / h$
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