Question

A man can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find his speed of rowing in still water.

2 points

4 km/hr

6km/hr

8 km/hr

2 km/hr
​

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:rowing=6\:km/hr}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• A man can row 20 km downstream in 2 hours
• The man ca row 4 km upstream in 2 hours

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Speed of rowing in still water

$\Large{\underline{\underline{\bf{Solution:}}}}$

⇝ Let the speed of rowing be x km/hr

⇝ Let the speed of the river be y km/hr

⇝ Speed while rowing upstream = x - y km/hr

⇝ Speed while rowing downstream = x + y km/hr

⇝ We know that,

    Time = Distance/Speed

⇝ Hence by first case,

    $\sf{\dfrac{20}{x+y}=2}$

⇝ By second case,

    $\sf{\dfrac{4}{x-y}=2}$

⇝ Let 1/x + y = p, 1/x - y =q

⇝ Hence,

   20p = 2

        p = 2/20

        p = 1/10

⇝ Also,

    4q = 2

       q = 2/4

       q = 1/2

⇝ But we know that 1/x + y = p,

    x + y = 10

    y = 10 - x ----(1)

⇝ Also, 1/x _ y = q

    x - y = 2

⇝ Substitute the value of y from equation 1

   x - (10 - x) = 2

   x - 10 + x = 2

   2x = 12

     x = 12/2

     x = 6

⇝ Hence the speed of rowing is 6 km/hr

    $\boxed{\bold{Speed\:of\:rowing=6\:km/hr}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

⇝ A linear equation in two variables can be solved by

• Substitution method
• Elimination method
• Cross multiplication method

Answer 2

Answer :-

✳Speed of rowing in still water = 6 km/hr

★ Speed of stream = 4 Km/hr

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★ Concept :-

Here the of Linear Equations have been used. This is nearly similar to the Linear Equations in Two Variables. There we use two different variables but her what we do is, we change the value of one variable into other so that a quadratic equation is formed and we can get our answer. This is formulated as :-

ax + by + c = 0

• Time = Distance / Speed

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★ Solution :-

• Let the speed of the man of rowing in still water be 'x' Km/hr.

• Let the speed od the stream be 'y' Km/hr.

We know that,

▶ Speed of the body moving Upstream = Original Speed - Speed of the stream =

(x - y) Km/hr

▶Speed of the body moving downstream = Orginal Speed - Speed of the stream = (x + y) Km/hr

________________________________

According to the question,

✏ { (20) / (x + y) } = 2 ...(i)

And,

✏ {(4) / (x - y)} = 2 .... (ii)

From equation (i) , we get,

✒ 2(x + y) = 20

✒ 2x + 2y = 20

Dividing both sides by 2 , we get,

✒ x + y = 10

✒ y = 10 - x ...(iii)

From equation (ii) we get,

✒ 2(x - y) = 4

✒ 2x - 2y = 4

Dividing both sides by 2 , we get,

✒ x - y = 2 ...(iv)

________________________________

From equation (iii) and equation (iv) we get,

▶ x - (10 - x) = 2

▶ x - 10 + x = 2

▶ 2x = 2 + 10

▶ 2x = 12

▶ x = {12} / {2}

▶ x = 6

Hence the speed of the man rowing in still water = 6 Km/hr

Now from equation (iii), we get,

✒ y = 10 - x

✒ y = 10 - 6 = 4

Hence speed of the stream = 4 Km/hr

✳ Hence the speed of man rowing in still water = 6 km / hr

_______________________________

★ Verification :-

For verifying that if the answer we got is correct or not, we just have to simple apply the values we got into the equations we formed. If our answer is correct,the equations will satisfy.

Case I :-

=> 2(x + y) = 20

=> 2(6 + 4) = 20

=> 2(10) = 20

=> 20 = 20

Clearly, LHS = RHS

Case II :-

=> x - y = 2

=> 6 - 4 = 2

=> 2 = 2

Clearly, LHS = RHS

Since both the conditions satisfy, our answer is correct.

___________________________

★ More to know :-

• Linear Equations are the equations formed with constants and variables that gives us a graph on solving the values. They can be solved by :-

• Substitution Method
• Elimination Method
• Reducing the pair
• Cross Multiplication