Question

A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.​

Answer 1

★Given:-

• A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours.
• In the same time it covers a distance of 12 km upstream and 36km downstream.

★To find:-

• The speed of the boat in still water and that of the stream.

★Solution:-

Let,

• Speed of boat in still water = x kmph.

Then,

• Downstream speed = (x + y) kmph
• Upstream speed = (x-y) kmph

Given that the motorboat covers a distance of 16km upstream and 24km downstream in 6 hours.Therefore,

=> 24/(x+y) + 16/(x-y) = 6_____(1)

Also, In the same time it covers a distance of 12 km upstream and 36km downstream.Therefore,

=> 36/(x+y) + 12/(x-y) = 6_____(2)

Let,

• 1/(x+y) = u
• 1/(x-y) = v

Putting the values in the above two equations,

Equation (1) becomes :

»24u + 16v = 6

»3(12u + 8v) = 6

»12u + 8v = 6/3

»12u + 8v = 3_____(3)

Equation (2) becomes :

»36u + 12v = 6

»6(6u + 2v) = 6

»6u + 2v = 1______(4)

Multiplying equation (4) by 4,

» (6u + 2v = 1)×4

» 24u + 8v = 4______(5)

Subtracting (3) from (5),

24u + 8v = 4

12u + 8v = 3

- - -

12u = 1

» u = 1/12

Substituting the value of 'u' in equation(4),

» 6u + 2v = 1

» 6(1/12) + 2v = 1

» 1/2 + 2v = 1

» 4v = 1

» v = 1/4

Now, we have,

• 1/(x+y) = u
• 1/(x-y) = v

Therefore,

=> 1/(x+y) = 1/12

=> x + y = 12

And,

=> 1/(x-y) = 1/4

=> x - y = 4

Also we have,

• Downstream speed = (x + y) kmph

• Upstream speed = (x-y) kmph

Therefore,

Speed of boat in still water = 12 - 4 = 8kmph.

Speed of stream = 4kmph.

___________________

Answer 2

Question:

A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.

Given:

• A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours.
• In the same time it covers a distance of 12 km upstream and 36km downstream.

To find:

• The speed of the boat in still water and that of the stream.

Solution:

Let,

• Speed of boat in still water = x kmph.

Then,

• Downstream speed = (x + y) kmph
• Upstream speed = (x-y) kmph

➪ Given that the motorboat covers a distance of 16km upstream and 24km downstream in 6 hours.

Therefore,

$\frac{24}{(x + y)} + \frac{16}{(x - y)} = 6 \: \:$

---------(1)

Also, In the same time it covers a distance of 12 km upstream and 36km downstream.

Therefore,

$\frac{36}{(x + y)} + \frac{12}{(x - y)} = 6$

----------(2)

Let,

$\frac{1}{(x + y)} = u$

$\frac{1}{(x - y)} = v$

Putting the values in the above two equations,

Equation (1) becomes :

$24u + 16v = 6$

$3(12u + 8v) = 6$

$12u + 8v = \frac{6}{3}$

$12u + 8v = 3$

----------(3)

Equation (2) becomes..

$36u + 12v = 6$

$6(6u + 2v) = 6$

$6u + 2v = 1$

-----------(4)

Multiply Equation (4) wíth 4.

$(6u + 2v = 1) \times 4$

$24u + 8v = 4$

-------------(5)

subtract Equation (3) from (5)

Subtracting (3) from (5),

24u + 8v = 4

12u + 8v = 3

- - -

__________

12u = 1

__________

$u = \frac{1}{12}$

Substating the value of 'u' in equation (4).

$6u + 2v = 1$

$6( \frac{1}{2} ) + 2v = 1$

$\frac{1}{2} + 2v = 1$

$4v = 1$

$v = \frac{1}{4}$

Now,

$\frac{1}{(x + y)} = u$

$\frac{1}{(x - y)} = v$

$\frac{1}{(x + y)} = \frac{1}{12}$

$x + y = 12$

&

$\frac{1}{(x - y)} = \frac{1}{4}$

$x - y = 4$

Also we have,

• Downstream speed = (x + y) kmph.

• Upstream speed = (x-y) kmph.

.'.

speed of boat in still water = 12- 4

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀= 8 kmph.

speed of stream = 4kmph.

$\sf\red{hope\:it\:helps\:you}$