A man can row 24 km upstream and 54 km downstream in 6 hours. He can also row 36 km upstream and 48 km downstream in 8 hours. What is the speed of the man in still water?

$frac{{24}}{u} + frac{{54}}{v} = 6 ldots ldots ldots left( 1 ight)$

$frac{{36}}{u} + frac{{48}}{v} = 8 ldots ldots .left( 2 ight)$

eqn (1) × 3 – eqn (2) × 2

$frac{{72}}{u} + frac{{162}}{v} = 18$

$frac{{72}}{u} + frac{{96}}{v} = 16$

$frac{{66}}{v} = 2$

????=33

Put in the eqn (1)

$frac{{24}}{u} + frac{{54}}{{33}} = 6$

????=5.5

∴ Speed of the man in still water

= $frac{{33 + 5.5}}{2} = frac{{38.5}}{2}$

= 19.25 kmph