Question

A streamer covers the distance between two parts in 3 hours when it goes downstream and 5 hours when it goes upstream. Find the speed of the streamer upstream if the stream flows at 3km/h.​

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Linear Equations in Two Variable has been used. According to this if the value of one variable is made to depend on other, we can find both of them using constant terms. Here we will take the speed of streamer and the distance between the places as variables.

→ Distance = Speed × Time

Let's do it !!

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★ Question :-

A streamer covers the distance between two parts in 3 hours when it goes downstream and 5 hours when it goes upstream. Find the speed of the streamer upstream if the stream flows at 3km/hr.

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★ Solution :-

Given,

» Time taken while going upstream = 5 hours

» Time taken while going downstream = 3 hours

» Speed of the stream = 3 Km/hr

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

• Let the distance between the two places be 'y' Km.

Thus,

→ Speed of streamer while going upstream = (x - 3) Km/hr

→ Speed of the streamer while going downstream = (x + 3) Km/hr

Then, according to the question :-

~ Case I :-

⌬ (x - 3) × 5 = y

⌬ 5x - 15 = y

⌬ y = 5x - 15 ... (i)

~ Case II :-

⌬ (x + 3) × 3 = y

⌬ 3x + 9 = y

⌬ y = 3x + 9 ... (ii)

From equation (i) and (ii), we get,

⌬ 5x - 15 = 3x + 9

⌬ 5x - 3x = 9 + 15

⌬ 2x = 24

$\: \: \longrightarrow \: \: \bf{x \: = \: \dfrac{24}{2} \: = 12}$

$\: \: \: \huge{\boxed{\boxed{x \: = \: 12 \: Kmhr^{-1}}}}$

• Hence, the speed of the streamer = x = 12 Km/hr

• Hence, the speed of the streamer in Upstream = (x - 3) Km/hr

= (12 - 3) Km/hr

= 9 Km/hr.

Now using the value of x and equation (ii), we get,

⌬ y = 3x + 9

⌬ y = 3(12) + 9

⌬ y = 36 + 9

⌬ y = 45

$\: \: \: \huge{\boxed{\boxed{y \: = \: 45 \: Km}}}$

• Hence, the distance between the two places = y = 45 Km

$\: \: \boxed{\rm{\mapsto \: \: Thus, \: the \: speed \: of \: the \: streamer \: is \: \underline{12 \: Kmhr^{-1}} \: and \: the \: distance \: between \: the \: places \: is \: \underline{45 \: Km.}}}$

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$\: \: \underline{\underline{\rm{\Longrightarrow \: \: Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}$

For verification, we need to simply apply the values we got into the equations we formed. Then,

~ Case I :-

=> y = 5x - 15

=> y = 5(12) - 15

=> 45 = 60 - 15

=> 45 = 45

Clearly, LHS = RHS

=> y = 3x + 9

=> 45 = 3(12) + 9

=> 45 = 36 + 9

=> 45 = 45

Clearly, LHS = RHS

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.

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$\: \: \: \boxed{\boxed{\underline{\mapsto \: \: Reference \: as \: Supplementary \: Information}}}$

• Polynomials are the equations formed using constant and variable terms of several degrees.

• Linear Polynomial
• Quadratic Polynomial
• Cubic Polynomial
• Bi - Quadratic Polynomial

• Linear Equations are the equations formed using constant and variable terms of single degrees.

• Linear Equation in One Variable
• Linear Equation in Two Variable
• Linear Equation in Three Variable

Answer 2

Given :

• A streamer covers the distance between two parts in 3 hours when it goes downstream and 5 hours when it goes upstream.

To find :

• Find the speed of the streamer upstream if the stream flows at 3km/h.​

SoIution :

Let the distance between two parts be n km.

∵ Speed = Distance/Time

∴ Speed in downstream = n/3 km/h

∴ Speed in upstream = n/5 km/h

Speed of current in stream = 3 km/h

Now using formuIa,

2 * speed of current = Speed(Downstream) - Speed(upstream)

⇒ 2 * 3 = n/3 - n/5

⇒ 6 = (5n - 3n)/15

⇒ 6 = 2n/15

⇒ 6 * 15 = 2n

⇒ 90 = 2n

⇒ n = 90/2

⇒ n = 45 km

∴ Speed of streamer in upstream = n/5

                                                        = 45/5

                                                         = 9 km/h

Therefore,

Speed of streamer in upstream = 9 km/h