Question

A steamer goes downstream from one port to another in 6 hours. It covers
the same distance upstream in 7 hours. If the speed of the stream be 2 km/hr, find the
speed of the steamer in still water.​

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:the\:steamer=26\:km/hr}}$

Step-by-step explanation:

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

• Steamer goes downstream in 6 hours
• Steamer goes upstream in 7 hours
• Speed of the stream = 2 km/hr

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

• Speed of the steamer in still water

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

➟ Here we are given that the steamer covers same distance downstream and upstream in 6 and 7 hours respectively.

➟ Let the speed of the steamer in still water be x km/hr.

➟ Hence,

   Speed while travelling upstream = (x - 2) km/hr

   Speed while travelling downstream = (x + 2) km/hr

➟ Now we know that,

    Distance = Speed × Time

➟ Hence in the first case,

    Distance travelled = (x + 2) × 6 ------(1)

➟ Now in the second case,

    Distance travelled = (x - 2) × 7 ------(2)

➟ From given we know that the LHS of equation 1 and equation 2 are equal.

➟ Hence,

   6 (x + 2) = 7 (x - 2)

   6x + 12 = 7x - 14

   7x - 6x = 12 + 14

   x = 26

➟ But we know that

   x = Speed of the steamer in still water

➟ Hence speed of the steamer is 26 km/hr.

Answer 2

★Speed of the steamer=26 km/hr

Step-by-step explanation:

Given :

• Steamer goes downstream in 6 hours

• Steamer goes upstream in 7 hours

•speed of the stream = 2 km/hr

To Find:

•Speed of the steamer in still water

Solution :

➡Here we are given that the steamer

covers same distance downstream and

upstream in 6 and 7 hours respectively.

➡Let the speed of the steamer in still water

be x km/hr.

➡Hence,

Speed while travelling upstream = (x - 2)

km/hr

Speed while travelling downstream = (x +2) km/hr

➡Now we know that,

Distance Speed x Time

➡Hence in the first case,

Distance travelled = (x + 2) × 6 ------(1)

➡Now in the second case,

Distance travelled = (x - 2) × 7 ---(2)

➡From given we know that the LHS of

equation 1 and equation 2 are equal.

➡Hence,

6 (x + 2) = 7 (x - 2)

6x + 12 = 7x - 14

7x-6x = 12 + 14

x = 26

➡But we know that

x = Speed of the steamer in still water

➡Hence speed of the steamer is 26 km/hr.