Question

A motorboat goes downstream and covers the distance between two ports in 5 hours and it returns back in 7 hours. If the speed of the stream is 2 km/h, find the speed of the boat in still water.

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:the\:boat=12\:km/hr}}$

Step-by-step explanation:

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

• The boat goes downstream in 5 hours
• The boat goes upstream in 7 hours
• Speed of the stream = 2 km/hr

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

• Speed of the boat in still water

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

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

→ Hence,

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

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

→ Let us take the distance between the two ports as y

→ Now we know that,

 Distance = Speed × Time

→ Hence, in the first case,

  y = (x + 2) × 5

  y = 10 + 5x-------(1)

→ In the second case,

  y = (x - 2) × 7

  y = 7x - 14

→ Now substitute the value of y from equation 1

  10 + 5x = 7x - 14

   7x - 5x = 10 + 14

   2x = 24

     x = 12

→ Hence speed of the boat in still water is 12 km/hr

  $\boxed{\bold{Speed\:of\:the\:boat=12\:km/hr}}$

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

→ A linear equation in two variables can be solved by

• Substitution method

• Elimination method
• Cross multiplication method