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 ?

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 ?
1). 18.75 km/h
2). 19.25 km/h
3). 17.65 km/h
4). 15.55 km/h

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Guest · Answer 1 · 2019-04-06 11:22:28

Solution

Let speed of man upstream = $x$ km/h

and speed of man downstream = $y$ km/h

Acc to ques,

=> $\frac{24}{x} + \frac{54}{y} = 6$

=> $\frac{4}{x} + \frac{9}{y} = 1$ -------------Eqn(1)

and $\frac{36}{x} + \frac{48}{y} = 8$

=> $\frac{9}{x} + \frac{12}{y} = 2$ -------------Eqn(2)

Solving equations (1) & (2), we get :

=> $x = \frac{11}{2}$ and $y = 33$

$\therefore$ Speed of man in still water = $\frac{1}{2}$ (downstream + upstream)

= $\frac{1}{2} (\frac{11}{2} + 33)$

= $\frac{77}{4} = 19.25$ km/h

Guest · Answer 2 · 2019-04-18 11:03:13