Question

a boat covers 32 km upstream and 36 km downstream in 7 hrs also it covers 40 km upstream and 48 km downstream in 9 hrs. find the speed of the boat in still water and that of the stream.

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:stream=2\:km/hr}}$

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

Step-by-step explanation:

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

• Boat travels 32 km upstream and 36 km downstream in 7 hours
• Boat travels 40 km upstream and 48 km downstream in 9 hours

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

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

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

→ Let the speed of boat in still water be x km/hr

→ Let speed of stream be y km/hr

→ Hence,

  Speed of boat while travelling upstream = ( x - y ) km/hr

  Speed of boat while travelling downstream = ( x + y ) km/hr

→ Time taken is given by the equation,

  Time = Distance/Speed

→ By first case given,

  $\dfrac{32}{x-y}+\dfrac{36}{x+y} =7----(1)$

→ By second case given,

  $\dfrac{40}{x-y} +\dfrac{48}{x+y} =9----(2)$

→ Let us take 1/x-y as p and 1/x+y as q

→ Hence equation 1 and 2 changes to

  32p + 36q = 7 -----(3)

  40p + 48q = 9 ----(4)

→ Multiply equation 3 by 4 and equation 4 by 3

→ Hence we get,

  128p + 144q = 28---(5)

  120p + 114q = 27----(6)

→ Solving equation 5 and 6 by elimination method,

  8p = 1

    p = 1/8

→ Substitute the value of p in equation 4

  40 × 1/8 + 48q = 9

  5 + 48q = 9

        48q = 4

             q = 1/12

→ Now we know that p = 1/x-y and q = 1/x+y

→ Hence x-y = 1/p and x+y = 1/q

   x - y = 8

   x = 8 + y ----(7)

→ x + y =12

→ Substitute value of x from equation 7

  8 + y + y = 12

  2y = 4

    y = 2

→ Hence speed of stream is 2 km/hr

$\boxed{\bold{Speed\:of\:stream=2\:km/hr}}$

→ Substitute value of y in equation 7

  x = 8 + 2

  x = 10

→ Hence the speed of boat in still water is 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

Answer 2

Answer:

Paranormal events are purported phenomena described in popular culture, folk, and other non-scientific bodies of knowledge, whose existence within these contexts is described as beyond the scope of normal scientific understanding.