Question

a boat covers 12 km upstream and 20 km downstream in 5 hours. it can go 16 km upstream and 10 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.​

Answer 1

Answer:

Speed of Boat in still water $\longrightarrow$ 7km/h

Speed of the stream $\longrightarrow$ 3km/h

Step-by-step explanation:

Let the speed of the boat in still water be 'x'

Let the speed of the stream be 'y'

Upstream is when the boat goes against the flow of water. Hence the equation turns out to be negative.

∴ $\boxed{\sf Upstream = \dfrac{1}{x \ - \ y}}$

Downstream is when the boat goes along the flow of water. Hence the equation turns out to be positive.

∴ $\boxed{\sf Downstream\ =\dfrac{1}{x \ + \ y}}$

According the question,

$\sf\frac{12}{x \ - \ y}$ + $\sf\frac{20}{x \ + \ y}$ = 5

$\sf\frac{16}{x \ - \ y}$ + $\sf\frac{10}{x \ + \ y}$ = 5

Let us assume that,

$\sf\dfrac{1}{x \ - \ y}= a$ and $\sf\dfrac{1}{x \ + \ y}= b$

Substituting these values in the formed equations we get,

12a + 20b = 5 → 1

16a + 10b = 5 → 2

Mulitply Equation 2 by 2

→ 32a + 20b = 10 → 3

On Subtracting Equation 1 from Equation 3 we get,

32a + 20b = 10

(-)    (-)         (-)

12a + 20b = 5

____________

20a = 5

$\sf a = \dfrac{5}{20}$

$\boxed{\sf a = \sf\frac{1}{4}}$ → 4

Substitute the value of 'a' in Equation 1.

12a + 20b = 5

12 $\sf(\frac{1}{4})$ + 20b = 5

3 + 20b = 5

20b = 5 - 3

20b = 2

$\sf b = \dfrac{2}{20}$

$\boxed{\sf b = \sf\frac{1}{10}}$ → 5

Now we substitute the values 'a' in  $\sf\dfrac{1}{x \ - \ y}$ and 'b' in  $\sf\dfrac{1}{x \ + \ y}$

$\sf\dfrac{1}{x \ - \ y} = a$

$\sf\dfrac{1}{x \ - \ y} = \dfrac{1}{4}$

x - y = 4 → 6

$\sf\dfrac{1}{x \ + \ y} = b$

$\sf\dfrac{1}{x \ + \ y} = \dfrac{1}{10}$

x + y = 10 → 7

Adding equation 6 and 7 we get,

x - y = 4

x + y = 10

2x = 14

x = $\sf\frac{14}{2}$

∴ x = 7

Substitute the value of 'x' in equation 6.

x - y = 4

7 - y = 4

7 - 4 = y

∴ y = 3

∴ The speed of the Boat in Still water is 7km/h.

∴ The speed of the stream is 3 km/h.

Answer 2

Answer:

x - y = 4

x + y = 10

2x = 14

∴ x = 7

Substitute the value of 'x' in equation 6.

x - y = 4

7 - y = 4

7 - 4 = y

∴ y = 3

∴ The speed of the Boat in Still water is 7km/h.

∴ The speed of the stream is 3 km/h.