Question

A boat gives 24km down stream and return in 5hrs but takes 8hrs to 36km downsteam and 40 km upstream find the speed in of boat and speed of stream.
pls help me will mark as brainlist answer

Answer 1

Answer:

x= 10

y=2

Step-by-step explanation:

24/x+y +24/x-y =5 ----×3

36/x+y + 40/x-y =8 ------×2

by solving both equation

x-y ===8

×+y===12

so

x=10

y=2

Answer 2

Answer:

Speed of the boat in still water = 10 km/hr.

Speed of stream = 2 km/hr.

Correction in the Question:

A boat goes 24km downstream & upstream and return in 5hrs but takes 8hrs to go 36km downstream and 40 km upstream. Find the speed of the boat in still water and the speed of the stream.

Step-by-step explanation:

Let the speed of the boat in still water be "x".

Let the speed of the stream be "y".

Upstream: Going against the flow of water.

Downstream: Going along with the flow of water.

The speed taken to go upstream will be x - y.  (Since they're in opposite directions)

The speed taken to go downstream will be x + y. (Since they're in the same direction)

ATQ:

The boat goes 24 km upstream and downstream in 5 hours. Adding the time taken to go upstream and downstream will give us 5 hours, therefore we get:

$\rm \Longrightarrow Time \ taken \ to \ go \ upstream + Time \ taken \ to \ go \ downstream = 5 \ hours$

Using Time = Distance/Speed we get:

$\rm \Longrightarrow \dfrac{24}{x - y} + \dfrac{24}{x + y} = 5 \ hours$

Let this be Equation(1) ↑

ATQ, The boat goes 36 km downstream and 40km upstream in 8 hours. Adding the time taken to go upstream and downstream will give us 8 hours, therefore we get:

$\rm \Longrightarrow Time \ taken \ to \ go \ upstream + Time \ taken \ to \ go \ downstream = 8 \ hours$

$\rm \Longrightarrow \dfrac{40}{x - y} + \dfrac{36}{x + y} = 8 \ hours$

Let this be Equation(2) ↑

Now, let us take 1/(x - y) = a, and 1/(x + y).

Applying this to Equation 1 and Equation 2 we get:

$\rm \Longrightarrow 24a + 24b = 5$  → Eq(3)

$\rm \Longrightarrow 40a + 36b = 8$ → Eq(4)

Multiply Eq(3) by 40 and Eq(4) by 24.

Eq(3) × 40 = 960a + 960b = 200 ➝ Eq(5)

Eq(4) × 40 = 960a + 864b = 192 ➝ Eq(6)

Subtracting Eq(5) from Eq(6) we get:

➝ 960a + 864b - [960a + 960b] = 192 - 200

➝ 960a + 864b - 960a - 960b = -8

➝ 864b - 960b = -8

➝ -96b = -8

➝ 96b = 8

➝ b = 8/96

➝ b = 1/12

Substitute the value of 'b' in Eq(5).

➝ 960a + 960b = 200

➝ 960a + 960(1/12) = 200

➝ 960a + 80 = 200

➝ 960a = 200 - 80

➝ 960a = 120

➝ a = 120/960

➝ a = 1/8

Now, substitute the value of "a" and "b" in 1/(x - y) and 1/(x + y) respectively.

Sub "a" in 1/(x - y).

$\rm \Longrightarrow a = \dfrac{1}{x - y}$

$\rm \Longrightarrow \dfrac{1}{8} = \dfrac{1}{x - y}$

$\rm \Longrightarrow x - y = 8$ ➝ Eq(7)

Now, Sub "b" in 1/(x + y).

$\rm \Longrightarrow b = \dfrac{1}{x + y}$

$\rm \Longrightarrow \dfrac{1}{12} = \dfrac{1}{x + y}$

$\rm \Longrightarrow x + y = 12$  ➝ Eq(8)

Adding Eq(8) & Eq(7) we get:

➝ x - y + x + y = 8 + 12

➝ x + x = 20

➝ 2x = 20

➝ x = 20/2

➝ x = 10

Substitute the value of "x" in Eq(7)

➝ x - y = 8

➝ 10 - y = 8

➝ 10 - 8 = y

➝ 2 = y

➝ y = 2

∴ Speed of the boat in still water = 10 km/hr.

∴ Speed of stream = 2 km/hr.