Question

A man can row 30km upstream and 45km downstream in 7hours.also,he can row 20km upstream and 35km downstream in 5hours. Find the speed of the main i still water and the speed of the current

Answer 1

Answer :

Speed of man = 11.25 km/h

Speed of current = 3.75 km/h

Solution :

Let the speed of man is x and that of current is y

Downstream speed will be (x + y)

Upstream speed will be (x - y)

He travels 30km upstream and 45km downstream in 7 hrs.

$\frac{30}{x - y} + \frac{45}{ x + y} = 7$

He travels 20km upstream and 35 km downstream in 5 hrs.

$\frac{20}{x - y} + \frac{35}{x + y} = 5$

Let, $\frac{1}{x - y} = p$, $\frac{1}{x + y} = q$

30p + 45q = 7

20p + 35q = 5

Solving these equations, We get

$q = \frac{1}{15}$ then $p = \frac{2}{15}$

$x - y = 7.5 \\ x + y = 15$

Solving the above equations, we get

x = 11.25 kmph

y = 3.75 kmph