Question

A boat travels 60km downstream and 20 km upstream in 4 hours that same boat travels 40km downstream 40 km upstream in 6hours what is the speed of the stream
plz answer right ..its necessary
With step to step explanation​

Answer 1

Given :-

◉ A boat travels 60km downstream and 20km upstream in 4 hours. That same boat travels 40km downstream and 40km upstream in 6 hours.

To Find :-

◉ Speed of the stream

Solution :-

Let the speed of boat in still water and speed of stream be x and y respectively.

Note :- While going upstream the flow of water would be against the motion of boat and therefore the speed while going upstream would be x - y

Also, While going downstream the direction of flow of water would be in the direction of motion of boat and hence the speed would be x + y

According to the question,

Case 1 :-

while going upstream:

• Distance covered, d₁ = 20km
• Speed, s₁ = x - y

⇒ Time taken = Distance/Speed

⇒ t₁ = 20 / (x - y) ...(1)

while going downstream:

• Distance covered, d₂ = 60km
• Speed, s₂ = x + y

⇒ Time taken = Distance/Speed

⇒ t₂ = 60 / (x + y) ...(2)

According to the question, It took the boat 4 hrs to go downstream and upstream.

∴ t₁ + t₂ = 4

⇒ 20/(x - y) + 60/(x + y) = 4

Let 1/(x - y) = A and 1/(x + y) = B ...(3)

Then, the linear equation becomes,

⇒ 20A + 60B = 4 ...(4)

Case 2 :-

while going upstream:

• Distance covered, d₃ = 40km
• Speed, s₃ = x - y

⇒ Time taken = Distance/Speed

⇒ 40 / (x - y)

⇒ 40/(x - y)

⇒ t₃ = 40A [ from (3) ]

while going downstream:

• Distance covered, d₂ = 40km
• Speed, s₂ = x + y

⇒ Time taken = Distance/Speed

⇒ 40 / (x + y)

⇒ t₄ = 40B ...(5)

According to the question, It took the boat 6 hours to go upstream and downstream as well.

⇒ t₃ + t₄ = 6

⇒ 40A + 40B = 6 ...(6)

Multiply (4) by 2 to make the coefficient of A equal to 40.

⇒ 40A + 120B = 8 ...(7)

Subtract (6) from (2), we have

⇒ 40A + 120B - 40A - 40B = 8 - 6

⇒ 80B = 2

⇒ B = 1/40 ...(8)

Substitute value of B in (6)

⇒ 40A + 40×1/40 = 6

⇒ 40A + 1 = 6

⇒ 40A = 5

⇒ A = 1/8 ...(9)

But from (1), A = 1(x - y) & B = 1/(x + y)

∴ 1(x - y) = 1/8 [ from (9) ]

⇒ x - y = 8 ...(10)

Also,

⇒ 1(x + y) = 1/40 [ from (8) ]

⇒ x + y = 40 ...(11)

Adding (10) & (11) , we have

⇒ x + y + x - y = 40 + 8

⇒ 2x = 48

⇒ x = 24

Substituting for x = 24 in (10)

⇒ 24 - y = 8

⇒ y = 24 - 8

⇒ y = 16

Hence,

• Speed of boat = 24 km/hr
• Speed of stream = 16 km/hr

Answer 2

Answer:-

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• Given:-

Distance travelled by boat in Downstream = $\bf{60 \: km}$

Distance travelled by boat in Upstream = $\bf{20 \: km}$

Time taken by the boat = $\bf{4 \: hours}$

Also,

Distance travelled by the same boat in Downstream = $\bf{40 \: km}$

Distance travelled by the same boat in Upstream = $\bf{40 \: km}$

Time taken by the same boat = $\bf{6 \: hours}$

• To Find:-

Speed of the stream =$\bf{?}$

• Solution:-

Let speed of boat in still water is $\bf{x \: km/hr}$ and speed of boat in stream water is $\bf{y \: km/hr}$

Then;

Speed of boat in downstream =$\bf(x + y) km/hr$

Speed of water in upstream =$\bf (x - y) km/hr$

We know that..

$\boxed{Time = \dfrac{Distance}{Speed}}$

_____________________________

» CASE 1:-

The boat travels 20 km upstream and 60 km downstream in 4 hours.

$\implies{\dfrac{20}{x\:-\:y}} + \dfrac{60}{x\:+\:y}= 4$

Let $\frac{1}{x\:-\:y}$= a and $\frac{1}{x\:+\:y}$=b

$\implies 20a + 60b = 4$

$\implies\bf{10a + 30b = 2} \: \: \: \: \: \: \longrightarrow\bf[eq.1]$

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» CASE 2:-

The same boat travels 40 km upstream and 40 km downstream in 6 hours.

$\implies \dfrac{40}{x\:-\:y} + \dfrac{40}{x\:+\:y}= 6$

$\implies 40a + 40b = 6$

$\implies\bf{20a + 20b = 3} \: \: \: \: \: \: \longrightarrow\bf[eq.2]$

____________________________

Multiplying [eq.1] with 2 :-

$\implies\bf{20a + 60b = 4} \: \: \: \: \: \: \longrightarrow\bf[eq.3]$

Subtracting [eq.2] from [eq.3]:-

$\implies 20a + 60b - (20a + 20b) = 4 - 3$

$\implies 20a + 60b - 20a - 20b = 1$

$\implies 40b = 1$

$\implies\bf{b = \dfrac{1}{40}}$

Putting value of of b in [eq.1]:-

$\implies 10a + 30 (\dfrac{1}{40}) = 2$

$\implies 10a + \dfrac{3}{4} = 2$

$\implies 10a = 2 - \dfrac{3}{4}$

$\implies 10a = \dfrac{8-3}{4}$

$\implies 10a = \dfrac{5}{4}$

$\implies a = \dfrac{5}{4 \times 10}$

$\implies\bf{a = \dfrac{1}{8}}$

___________________________

Now..

$\dfrac{1}{x\:-\:y} = \dfrac{1}{8}$

and

$\dfrac{1}{x\:+\:y} = \dfrac{1}{40}$

$\implies x - y = 8 \: \: \: \: \: \: \longrightarrow\bf[eq.4]$

and

$\implies x + y = 40 \: \: \: \: \: \: \longrightarrow\bf[eq.5]$

• Adding [eq.4] and [eq.5]:-

$\implies(x - y) + (x + y) = 8 + 40$

$\implies x - y + x + y = 48$

$\implies 2x = 48$

$\implies x = \dfrac{48}{2}$

$\implies\bf{ x = 24}$

•Putting value of x in [eq 5]:-

$\implies x+ y = 40$

$\implies 24 + y = 40$

$\implies y = 40 - 24$

$\implies\bf{y = 16}$

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$\therefore$Speed of boat in still water is $\bf{24 \: km/hr}$ and speed of boat in stream water is $\bf{16 \: km/hr}$