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.
A) Speed of rowing in still water: 10 km/hr and the speed of the current: 5 km/hr.
B) Speed of rowing in still water: 8 km/hr and the speed of the current: 7 km/hr.
C) Speed of rowing in still water: 18 km/hr and the speed of the current: 12 km/hr.
D) Speed of rowing in still water: 6 km/hr and the speed of the current: 4 km/hr.

Answer 1

Hint: Speed of river and rowing speed of a person in still water gets added in downstream and subtracted in upstream. This could be used to form equations using the given data.

Complete step-by-step answer:
Let us assume, the speed of Ritu rowing in still water is $x$ km/hr.
Also we make the assumption that the speed of current is $y$ km/hr.

We know that during upstream, the speed of Ritu rowing in still water and speed of the current of the river will be in opposite directions.
Hence the net speed at upstream will be $ = x - y$ km/hr

Similarly, during downstream, the speed of Ritu rowing in still water and speed of the current of the river will be in the same directions.
Hence the net speed at downstream will be $ = x + y$ km/hr

Now we need to use the given data in order to form equations in the assumed variables.
We know that,
${\text{Speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
Also, it is given that Ritu can row downstream 20 km in 2 hours.
 $
   \Rightarrow x + y = \dfrac{{20}}{2} = 10 \\
   \Rightarrow x + y = 10{\text{ ---- (1)}} \\
$

Similarly, it is given that Ritu can row upstream 4 km in 2 hours.
 $
   \Rightarrow x - y = \dfrac{4}{2} = 2 \\
   \Rightarrow x - y = 2{\text{ ---- (2)}} \\
$

Now we need to solve equations $(1)$and $(2)$.
Adding $(1)$ AND $(2)$,we get
$
  x + y + x - y = 12 \\
   \Rightarrow 2x = 12 \\
   \Rightarrow x = 6{\text{ km/hr}} \\
$

Subtracting $(1)$ AND $(2)$,we get
$
  x + y - x + y = 8 \\
   \Rightarrow 2y = 8 \\
   \Rightarrow y = 4{\text{ km/hr}} \\
$
Therefore, the speed of Ritu in still water is 6 km/hr and the speed of the current is 4 km/hr.
Hence option (D). Speed of rowing in still water: 6 km/hr and the speed of the current: 4 km/hr is the correct answer.

Note: The relation between speed in still water and speed with current should be kept in mind while solving problems like above. It is important to assume the correct variables and form an equal number of equations to solve them.