Question

Aman can row downstream 20km in 2hrs, and upstream 4 km in 2 hrs. Find his speed of rowing in still water, Also, find the speed of the current.

Answer 1

Answer:

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

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

Step-by-step explanation:

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

• Aman can row downstream 20 km in 2 hours and upstream 4 km in 2 hours.

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

• Speed of rowing in still water
• Speed of the current

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

➛ Let us assume the speed of rowing as x km/hr

➛ Let the speed of the current be = y km/hr

➛ Hence,

   Speed while rowing upstream = (x - y) km/hr

   Speed while rowing downstream = (x + y) km/hr

➛ We know that,

    Time = Distance/Speed

➛ By first case given,

    $\tt{\dfrac{20}{x+y}=2---(1)}$

➛ By second case given,

   $\tt{\dfrac{4}{x-y} =2----(2)}$

➛ Let 1/x + y = p, 1/x - y = q

➛ Hence,

   20p = 2

        p = 2/20

        p = 1/10

➛ But 1/x + y = 1/10

    x + y = 10

    x = 10 - y-----(3)

➛ Also,

   4q = 2

      q = 2/4

      q = 1/2

➛ But 1/x- y = 1/2

    x - y = 2

➛ Substitute the value of x from equation 3

    10 - y - y = 2

   -2y = -8

     y = 4

➛ Hence the speed of the current is 4 km/hr

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

➛ Substitute the value of y in equation 3

    x = 10 - 4

    x = 6

➛ Hence the speed of rowing in still water 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