Question

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Answer 1

$\huge{\underline{\underline{\bf concept}}}$

• We are given that Ritu can row her boat in downward direction of the stream (along the direction of stream) in 2 hours for 20km and can row upward direction of the stream (against the direction of stream) in 2 hours for 4km
• So, we need to assume two speeds, one of stream (y) and other of boat. (x)
• when she travels towards the direction of stream, her speed will increase so we will assume that speed as (x+y) km/hr
• when she travels against the direction of stream, her speed will decrease so we will assume that net speed as (x-y) km/hr
• Remember that the speed of the boat is always greater than the speed of stream

$\huge{\underline{\underline{\bf solution}}}$

we know that, $\sf Time = \dfrac{Distance}{Speed}$

According to the question:-

while traveling along the stream (downstream):-

$\implies\sf 2 = \dfrac{20}{x + y} \\ \\ \implies\sf 2(x + y) = 20 \\ \ \\ \implies\sf x + y = \frac{\cancel{20}}{\cancel{2}} = 10 \\ \\\implies \sf x + y = 10 \: - - - (1)$

while traveling against the stream (upstream)

$\implies\sf 2 = \dfrac{4}{x - y} \\ \\ \implies\sf \: 2(x - y) = 4 \\ \\ \implies\sf \: x - y = \frac{\cancel4}{\cancel2} = 2 \\ \\ \implies\sf \: x - y = 2 - - - (2)$

Adding both the equations, we get:-

$\implies\sf x + \cancel{y} + x - \cancel{y} = 10 + 2 \\ \\ \implies\sf \: 2x = 12 \\ \\ \implies\sf \: x = \frac{\cancel{12}}{\cancel2} = 6 \\ \\ \sf \therefore \: speed \: of \: rowing \: = 6km/hr \\ \\ \sf \: putting \: value \: of \: x \: in(1) \\ \\ \implies\sf \: 6 + y = 10 \\ \\ \implies\sf \: y \: = 4 \\ \\\sf \therefore \: speed \: of \: stream(current) = 4km/hr$