Question

Formulate the following problems as a pair of equations, and hence find their solutions:
(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her
speed of rowing in still water and the speed of the current.​

Answer 1

Answer:

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

$\bigstar{\bold{Speed\:of\:rowing=6\:km/hr}}$

Step-by-step explanation:

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

• Ritu can row downstream 20 km in2 hours
• Ritu can row upstream 4 km in 2 hours

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

• Speed of rowing in still water
• Speed of current

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

→ Let the speed of rowing be x km/hr

→ Let the speed of the current be y km/hr

→ The speed when rowing upstream = (x - y)km/hr

→ The speed when rowing doenstream = (x + y ) km/hr

→ We know that,

  Time = Distance/Speed

→ By the first case,

  $\dfrac{20}{x+y} =2$

→ Let 1/x+y = p

→ Hence,

  20p = 2

       p = 1/10

→ 1/x+y = 1/10

   x + y = 10

   x = 10 - y -----(1)

→ By second case,

  $\dfrac{4}{x-y} =2$

→ Let 1/x - y = q

→ Hence

  4q = 2

     q = 1/2

→ 1/x - y = 1/2

  x - y = 2

→ Substitute the value of x from equation 1

  10 - y - y =2

  10 - 2y = 2

      -2y = -8

         y = 4 km/hr

→ Hence speed of the current is 4 km/hr

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

→ Substitute the value of y in equation 1

  x = 10 - 4

  x = 6

→ Hence the speed of rowing is 6 km/hr

  $\boxed{\bold{Speed\:of\:rowing=6\:km/hr}}$

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

→ A linear equation in two variables can be solved by

• Substitution method
• Elimination method
• Cross multiplication method

Answer 2

Answer:

Let her speed in still water be x and speed of stream be y

Now, According to question  and using   time = speeddistance

⇒x+y20=2 and  x−y4=2

⇒x+y=10;x−y=2

⇒On solving we get x=6andy=4

⇒speed of Ritu in still water is 6km/hr and that of a stream is 4km/hr.

________________________________________________