Answer

Verified

431.4k+ views

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.

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.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

What organs are located on the left side of your body class 11 biology CBSE