Question

19. Ritu can row downstream 20 km in 2 hours and upstream 4 km in4 hours. Find her speed of rowing

in still water and speed of current.​

Answer 1

Answer :

• Ritu's speed of rowing in still water = 5 .5km/h
• Speed of current = 4.5 km/h

Given :

• Ritu can row downstream 20km in 2 hours and upstream 4km in 4 hours

To find :

• Ritu's Speed of rowing in still water
• Speed of current

Solution :

• Let the speed of Ritu rowing in still water be x km/h
• Let the speed of current be y km/h

Then,

• Upstream = (x - y) km/h
• Downstream = (x + y) km/h

According to question,  Given that ,

Ritu can row downstream 20km in 2 hours

• 2(x + y) = 20

➞ 2(x + y) = 20

➞ x + y = 20/2

➞ x + y = 10

x + y = 10 .... equation (1)

Ritu can row upstream 4km in 4 hours

• 4(x - y) = 4

➞ 4(x - y) = 4

➞ (x - y) = 4/4

➞ x - y = 1

x - y = 1 .... equation (2)

Equation are :

• x + y = 10 ....(1)
• x - y = 1 ....(2)

From equation (1)

➞ x + y = 10

➞ x = 10 - y

Now, putting x = 10 - y in equation (2) we get,

➞ x - y = 1

➞ (10 - y) - y = 1

➞ -2y = 1 - 10

➞ -2y = -9

➞ y = -9/-2

➞ y = 4.5

Now, putting y = 4.5 in equation (1) we get,

➞ x + y = 10

➞ x + 4.5 = 10

➞ x = 10 - 4.5

➞ x = 5.5

Hence,

• Ritu's speed of rowing in still water = 5.5 km/h
• Speed of current = 4.5 km/h

Answer 2

Given :

• Ritu can row downstream 20 km in 2 hours and upstream 4 km in 4 hours.

Find :

• Speed of rowing in still water and speed of current.

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Solution :

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• Let the speed of Ritu rowing in still water be x km/h.
• Let the speed of current be y km/h.

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Then,

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• Upstream = (x - y) km/h
• Downstream = (x + y) km/h

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$\underline{\bigstar\:\boldsymbol{According \;to \;the\: given \;Question\; :}}$

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• Ritu can row downstream 20 km in 2 hours.

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$\:\:\:\:\::\:\Longrightarrow\sf\:{2(x\:+\:y)\:=\:20}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:+\:y\:=\:{\dfrac{20}{2}}}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:+\:y\:=\:10}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{\bold{x\:+\:y\:=\:10}}\:{\blue{ ﹏﹏equ.1}}$

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Now,

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• Ritu can row upstream 4 km in 4 hours.

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$\:\:\:\:\::\:\Longrightarrow\sf\:{4(x\:-\:y)\:=\:4}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:-\:y\:=\:{\dfrac{4}{4}}}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:-\:y\:=\:1}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{\bold{x\:-\:y\:=\:1}}\:{\blue{ ﹏﹏equ.2}}$

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☆ Now, we get equations are :

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• $\sf\:{\bold{x\:+\:y\:=\:10}}\:{\blue{ ﹏﹏equ.1}}$
• $\sf\:{\bold{x\:-\:y\:=\:1}}\:{\blue{ ﹏﹏equ.2}}$

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From equation 1 :

$\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:+\:y\:=\:10}$

$\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:10\:-\:y}$

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Now, Putting x = 10 - y in equ.[ 2 ]

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:-\:y\:=\:1}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{(10\:-\:y)\:-\:y\:=\:1}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{-2y\:=\:1\:-\:10}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{-2y\:=\:-9}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{y\:=\:{\dfrac{-9}{-2}}}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{y\:=\:4.5}$

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Now, Putting y = 4.5 in equ.[ 1 ]

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:+\:y\:=\:10}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:+\:4.5\:=\:10}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:=\:10\:-\:4.5}$

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$\:\:\:\:\::\:\Longrightarrow\sf\:{x\:=\:5.5}$

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Therefore,

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• $\:\:{\sf{ Ritu's\:speed\:of\:rowing\:in\:still\:water\:is\:{\textsf{\textbf{5.5\:km/h }}}}}.$
• $\:\:{\sf{ Speed\:of\:current\:is\:{\textsf{\textbf{4.5\:km/h }}}}}.$

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