Question

A boat goes 24 km upstream and 28 km downstream in 6hrs.It goes 30 km upstream and 21 km downstream in 6 and half hours.Find the speed of boat and the speed of stream.

Class 10 CBSE
Pair of linear equations in two variables.​

Answer 1

Answer:

Let speed of boat in still water = x km/hr

Let speed of stream = y km/hr

Upstream speed = (x - y) km/hr

Downstream speed = (x + y) km/hr.

Case I :

x−y

24

+

x+y

28

=6

Let

x−y

1

=u &

x+y

1

=v

24u+28v=6 .....(1)

Case II :

x−y

30

+

x+y

21

=

2

13

30u+21v=

2

13

......(2)

Multiplying eq.(1) by 3 & eq.(2) by 4, we get

72u+84v=18

120u + 84v = 26

+48u=−8

u=

6

1

& v=

14

1

6

1

=

x−y

1

,

14

1

=

x+y

1

x−y=6 ......(3)

x+y=14 ......... (4)

On solving eq. (3) & (4)

x = 10 & y = 4

Hence, speed of boat in still water is 10 kmph.

Answer 2

Answer:

$\bigstar{\bold{Speed\:of\:stream=4\:km/hr}}$

$\bigstar{\bold{Speed\:of\:boat=10\:km/hr}}$

Step-by-step explanation:

$\Large{\underline{\underline{\sf{Given:}}}}$

• Boat goes 24 km upstream and 28 km downstream in 6 hours.
• Boat goes 30 km upstream and 21 km downstream in 6 and half hours = 13/2 hrs

$\Large{\underline{\underline{\sf{To\:Find:}}}}$

• Speed of boat
• Speed of stream

$\Large{\underline{\underline{\sf{Solution:}}}}$

➻ Let the speed of boat be x km/hr

➻ Let the speed of stream be y km/hr

➻ Speed of boat going upstream = ( x - y ) km/hr

➻ Speed of boat going downstream = ( x + y ) km/hr

➻ In the first case,

    $\dfrac{24}{x-y} +\dfrac{28}{x+y} =6-----equation\:1$

➻ In the second case,

    $\dfrac{30}{x-y} +\dfrac{21}{x+y} =\dfrac{13}{2} --------equation\:2$

➻ Let

   $\dfrac{1}{x-y} =p$        $\dfrac{1}{x+y}=q$

➻ Rewriting equation 1 and 2

   Equation 1 = 24p + 28q = 6

                         12p + 14q = 3--------equation 3

  Equation 2 = 30p + 21q = 13/2

                        60p + 42q = 13-------equation 4

➻ Multiplying equation 3 by 5

    60p + 70q = 15-------equation 5

➻ Solving equation 4 and 5 by elimination method

    60p + 70q = 15

    60p + 42q = 13

               28q = 2

                    q = 2/28 = 1/14

➻ Putting the value of q in equation 4

   60p + 42 × 1/14 = 13

   60p + 3 = 13

   60p = 10

        p = 1/6

➻ We know that

    $\dfrac{1}{x-y}=p=\dfrac{1}{6}$

    x - y = 6

    x = 6 + y ------equation 6

➻ We know that

    $\dfrac{1}{x+y} =q=\dfrac{1}{14}$

   x + y = 14

➻ Substituting the value of x from equation 6

    6 + y + y = 14

    2y = 8

      y = 4 km/hr

➻ Hence speed of stream is 4 km/hr

$\boxed{\bold{Speed\:of\:stream=4\:km/hr}}$

➻ Solving for x

    x + 4 = 14

    x = 10 km/hr

➻ Hence speed of boat = 10 km/hr

$\boxed{\bold{Speed\:of\:boat=10\:km/hr}}$

$\Large{\underline{\underline{\sf{Notes:}}}}$

➻ A linear equation in two variables can be solved by

• Substitution method
• Elimination method
• Cross multiplication method