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

Answer

Verified

380.7k+ views

Hint: Assume the variables for speed of Ritu in still water and speed of current and using the concept of spontaneity of flow of water and the formula \[speed=\dfrac{distance}{time}\] you will get simultaneous equations in these variables. After solving the equations you will get the final answer.

Complete step-by-step answer:

To find the speeds we should write the given values first, therefore,

Downstream distance = 20 Km.

Downstream Rowing Time = 2 hours.

Upstream distance = 4 Km.

Upstream rowing time = 2 hours.

As we have to find the Ritu’s speed of rowing in still water we will assume it to be ‘x’ and also we will assume the speed of current as ‘y’ therefore we will get,

Ritu’s speed in still water = x Km/hr. …………………………… (1)

Speed of current = y Km/hr. ……………………………. (2)

As we know that the water always flows from higher level to lower level and therefore while moving downstream the current will support Ritu and increase her speed i.e. speeds of both will add in.

Therefore from equation (1) and (2) we can write,

Downstream speed = (x+y) km/hr …………………………………………. (3)

To proceed further in the solution we should know the formula of speed given below,

Formula:

\[speed=\dfrac{distance}{time}\]

If we put the value of equation (3) and given values of downstream flow in above formula we will get,

\[\therefore \left( x+y \right)=\dfrac{20}{2}\]

\[\therefore x+y=10\] ………………………………………… (4)

Also, in upstream flow the current speed will oppose the speed of rowing in still water therefore we will get,

Upstream speed = (x-y) Km/hr. ………………………………………….. (5)

To proceed further in the solution we should know the formula of speed given below,

Formula:

\[speed=\dfrac{distance}{time}\]

If we put the value of equation (5) and given values of upstream flow in above formula we will get,

\[\therefore \left( x-y \right)=\dfrac{4}{2}\]

\[\therefore x-y=2\]………………………………………… (6)

By adding equation (4) and equation (6) we will get,

\[\begin{align}

& x+y=10 \\

& + \\

& x-y=2 \\

& \_\_\_\_\_\_\_\_\_\_\_\_ \\

& 2x+0=12 \\

\end{align}\]

\[\therefore 2x=12\]

\[\therefore x=\dfrac{12}{2}\]

Therefore, x = 6 Km/hr. ……………………………………….. (7)

If we put the value of equation (7) in equation (4) we will get,

\[\therefore 6+y=10\]

\[\therefore y=10-6\]

Therefore, y = 4 Km/hr. ……………………………………….. (8)

By using equation (1) (2) (7) and (8) we can write the final answer as,

Ritu’s speed in still water = x Km/hr = 6 Km/hr.

Speed of current = y Km/hr = 4 Km/hr.

Note: Don’t get confused in downstream and upstream flow. Use the concept of natural flow of water which is always from higher level to lower level. If you swap the concept then you will get the wrong answer.

Complete step-by-step answer:

To find the speeds we should write the given values first, therefore,

Downstream distance = 20 Km.

Downstream Rowing Time = 2 hours.

Upstream distance = 4 Km.

Upstream rowing time = 2 hours.

As we have to find the Ritu’s speed of rowing in still water we will assume it to be ‘x’ and also we will assume the speed of current as ‘y’ therefore we will get,

Ritu’s speed in still water = x Km/hr. …………………………… (1)

Speed of current = y Km/hr. ……………………………. (2)

As we know that the water always flows from higher level to lower level and therefore while moving downstream the current will support Ritu and increase her speed i.e. speeds of both will add in.

Therefore from equation (1) and (2) we can write,

Downstream speed = (x+y) km/hr …………………………………………. (3)

To proceed further in the solution we should know the formula of speed given below,

Formula:

\[speed=\dfrac{distance}{time}\]

If we put the value of equation (3) and given values of downstream flow in above formula we will get,

\[\therefore \left( x+y \right)=\dfrac{20}{2}\]

\[\therefore x+y=10\] ………………………………………… (4)

Also, in upstream flow the current speed will oppose the speed of rowing in still water therefore we will get,

Upstream speed = (x-y) Km/hr. ………………………………………….. (5)

To proceed further in the solution we should know the formula of speed given below,

Formula:

\[speed=\dfrac{distance}{time}\]

If we put the value of equation (5) and given values of upstream flow in above formula we will get,

\[\therefore \left( x-y \right)=\dfrac{4}{2}\]

\[\therefore x-y=2\]………………………………………… (6)

By adding equation (4) and equation (6) we will get,

\[\begin{align}

& x+y=10 \\

& + \\

& x-y=2 \\

& \_\_\_\_\_\_\_\_\_\_\_\_ \\

& 2x+0=12 \\

\end{align}\]

\[\therefore 2x=12\]

\[\therefore x=\dfrac{12}{2}\]

Therefore, x = 6 Km/hr. ……………………………………….. (7)

If we put the value of equation (7) in equation (4) we will get,

\[\therefore 6+y=10\]

\[\therefore y=10-6\]

Therefore, y = 4 Km/hr. ……………………………………….. (8)

By using equation (1) (2) (7) and (8) we can write the final answer as,

Ritu’s speed in still water = x Km/hr = 6 Km/hr.

Speed of current = y Km/hr = 4 Km/hr.

Note: Don’t get confused in downstream and upstream flow. Use the concept of natural flow of water which is always from higher level to lower level. If you swap the concept then you will get the wrong answer.

Recently Updated Pages

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

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

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

Trending doubts

The lightest gas is A nitrogen B helium C oxygen D class 11 chemistry CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Which place is known as the tea garden of India class 8 social science CBSE

What is pollution? How many types of pollution? Define it

Write a letter to the principal requesting him to grant class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE