Question

a steamer goes downstream from one part to another in 4 hours it cover the same distance upstream in 5 hours if the speed of the stream be 2 kilometre per hour find the distance between two parts​

Answer 1

SOLUTION :-

Let the speed of the streamer in still water be x.

Given that,

Speed of stream = 2 km/hr

Downstream :-

Speed downstream = ( x + 2 ) km/hr

Time taken = 4 h

Distance between two parts = 4 ( x + 2 ) km

Upstream :-

Speed upstream = ( x - 2 ) km/hr

Time taken = 5h

Distance between two parts = 5 ( x - 2 ) km

According to the question,

$\longrightarrow\sf 4(x+2)= 5(x-2)\\\\\longrightarrow 4x+8 = 5x-10 \\\\\longrightarrow 4x-5x= -10-8 \\\\\longrightarrow -x= -18 \\\\\longrightarrow\bf x = 18$

Speed of streamer in still water = 18 km/hr

Distance between two parts = 4 ( x + 2 )

                                                = 4 ( 18 + 2 )

                                                = 4 × 20

                                                = 80 km

Answer 2

Answer :-

★ Distance between two parts = 80 Km

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★Concept :-

Here the concept of Linear Equations in One Variable is used. These type of equation have one variable term and two constant terms with which we find solution. The standard form of Linear Equation in one Variable is given as :-

=> ax + b = c

• Distance = Speed × Time

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★ Solution :-

• Let the speed of the streamer be 'x' Km/hr.

Then,

Given,

▶Time taken to cover distance in downstream = 4 hours

▶ Time taken to cover distance in upstream = 5 hours

▶ Speed of the stream = 2 Km/hr

We know that,

» While going downstream, the speed of body and speed of stream is added. Then,

✏ Speed of streamer downstream =

(x + 2) Km/hr

» While going upstream, the speed of stream is subtracted from the speed of body. Then,

✏ Speed of streamer upstream = (x - 2) Km/hr

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Here its clearly given that journey takes place between two parts. So distance covered in upstream will surely be equal to distance covered in downstream. Equating the values in this, we get,

✒ 4(x + 2) = 5(x - 2)

✒ 4x + 8 = 5x - 10

Transposing the like terms opposite side, we get,

✒ 5x - 4x = 10 + 8

✒ x = 18 Km/hr

Hence, speed of streamer = 18 km/hr

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•Now the distance between two parts is given by,

→ Distance = Speed × Time

→ Distance = 4(x + 2)

→ Distance = 4(18 + 2)

→ Distance = 4 × 20

→ Distance = 80 Km

✳ Hence Distance between two parts = 80 Km

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★ More to know :-

• Graphical form of this equation : If we draw the graph of the equation we got, we see that the lime of equation intersects x-axis at 80.

• Linear Equation in Two Variables : are the form od equations where we get two sets of equations having two variable terms.

• Solution of Linear Equation in Two Variable :

• Substitution Method
• Elimination Method
• Reducing The Pair Method
• Cross Multiplication Method

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★ Verification of the above given problem :-

In order to verify if our solution is correct or not, we can just apply the value of x we got into that equation. Then,

=> 4(x + 2) = 5(x - 2)

=> 4(18 + 2) = 5(18 - 2)

=> 4 × 20 = 5 × 16

=> 80 = 80

Clearly, LHS = RHS.

This satisfies the equation.

Hence our solution is correct.