Question

boat covers some distance downstream in 6 hour while it cover the same distance upstream in 9 hours if the speed of boat in still water is 8 kilometre per hour find the speed of stream ​

Answer 1

The Speed of the stream is 1.6 Km/hr.

Given:

• Time in Downstream = 6 hours
• Time in Upstream = 9 hours
• Speed of Boat = 8 km/hr

Explanation

Let the speed of the Stream be x km/hr

Conditions

• Speed of the boat in downstream = (8+x) km/hr
• Speed of the boat in Upstream = (8-x) km/hr

$\dag{\boxed{\underline{\underline{\sf{ Distance_{(D)} = Time \times Speed }}}}}$

$\huge{ \circ }$ Distance taken Downstream

$\implies{\sf{ 6 \times (8+x)}} \\ \\ \implies{\sf{ 48 + 6x }}$

$\huge{ \circ }$ Distance taken Upstream

$\implies{\sf{ 9 \times (8-x)}} \\ \\ \implies{\sf{ 72 - 9x }}$

According to Question,

$\colon\implies{\sf{ 48 + 6x = 72 - 9x }} \\ \\ \\ \colon\implies{\sf{ 6x + 9x = 72 - 48 }} \\ \\ \\ \colon\implies{\sf{ \cancel{15} \ x = \cancel{25} }} \\ \\ \\ \colon\implies{\sf{ 3x = 5 }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{5}{3} } }} \\ \\ \\ \colon\implies{\boxed{\mathfrak\pink{ x = 1.6 \ km/hr }}}$

Hence,

• The Speed of the Stream is 1.6 km/hr