Question

a streamer goes downstream from one port to another in 9 hours and covers the same distance upstream in 10 hours. if the speed of stream be 3km/h find the speed of streamer in still water and distance between the ports ​

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:steamer=57\:km/hr}}$

$\bigstar{\bold{Distance=540\:km}}$

Explanation:

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

• Steamer goes downstream in 9 hours
• Steamer goes upstream in 10 hours
• Speed of stream = 3 km/hr

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

• Distance between the ports
• Speed of steamer in still water

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

⇝ Given that the speed of the stream is 3 km/hr

⇝ Let us assume the speed of the steamer in still water as x km/hr

⇝ Hence,

    Speed while travelling upstream = (x - 3) km/hr

    Speed while travelling downstream = (x + 3) km/hr

⇝ Now we know that,

    Distance = Speed × Time

⇝ Hence by first case,

    Distance = (x + 3) × 9

    Distance = 9x + 27-----(1)

⇝ Now by second case,

    Distance = (x - 3) × 10

    Distance = 10x - 30 -----(2)

⇝ Now by given, LHS of equations 1 and 2 are equal, hence RHS must also be equal.

   9x + 27 = 10x - 30

   10x - 9x = 27 + 30

    x = 57

⇝ Hence speed of steamer in still water is 57 km/hr.

    $\boxed{\bold{Speed\:of\:steamer=57\:km/hr}}$

⇝ Now substitute the value of x in equation 1,

    Distance = 9 × 57 + 27

    Distance = 540

⇝ Hence distance between the ports is 540 km.

    $\boxed{\bold{Distance=540\:km}}$