# 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

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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.

Last updated date: 26th May 2023

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