Question

a boat gose 30km upstream ANd 44 km downstream in 10 hours... in 13 hours it can go 40 km upstream and 55 km downstream .find the speed of the stream and that of boat in still water.

Answer 1

Answer:

answer 389 per km is the correct answer

Answer 2

Answer:

$\bigstar{\bold{Speed\:of\:boat\:in\:still\:water=8km/hr}}$

$\bigstar{\bold{Speed\:of\:stream=3\:km/hr}}$

Step-by-step explanation:

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

• Boat travels 30 km upstream and 44 km downstream in 10 hours
• Boat travels 40 km upstream and 55 km downstream in 13 hours

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

• Speed of stream
• Speed of the boat in still water

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

➜ Let us take the speed of the boat in still water as x km/hr

➜ Let the speed of stream be taken as y km/hr

➜ Hence,

    Speed of boat when travelling downstream would be ( x+ y) km/hr

    Speed of boat when travelling upstream would be (x - y) km/hr

➜ We know that,

    Time = Distance /Speed

➜ Hence by the first case,

    $\dfrac{30}{x-y} +\dfrac{44}{x+y} =10----equation\:1$

➜ By the second case,

    $\dfrac{40}{x-y} +\dfrac{55}{x+y}=13-----equation\:2$

➜ Now let, 1/x-y = p and 1/x+y = q

➜ Therefore, equation 1 ad 2 changes to

   30p + 44q = 10 -----equation 3

   40p + 55q = 13--------equation 4

➜ Multiply equation 3 by 4 and equation 4 by 3

  120p + 176q = 40 -----equation 5

  120p + 165q = 39------equation 6

➜ Solve equation 5 and 6 by elimination method,

              11q = 1

                 q = 1/11

➜ Put the value of q in equation 4

  40p + 55 × 1/11 = 13

  40p + 5 = 13

  40p = 8

      p = 8/40 = 1/5

➜ We know that 1/x-y = p and 1/x+y = q

    1/x-y = 1/5,  1/x+y = 1/11

    x - y = 5

    x + y = 11

➜ Solving for x and y by elimination method,

    2x = 16

      x = 8

➜ Hence speed of boat in still water = x km/hr = 8 km/hr

$\boxed{\bold{Speed\:of\:boat\:in\:still\:water=8km/hr}}$

➜ Substitute x in one of the above equations to find y

    8 + y = 11

          y = 11 - 8

          y = 3

➜ Hence speed of stream = y km/hr = 3 km/hr

$\boxed{\bold{Speed\:of\:stream=3\:km/hr}}$

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

A linear equation in two variables can be solved by:

• Substitution method
• Elimination method

• Completing the square method