Question

a man can row in still water at rate of 6 km per hour if the steam flow at rate of 2 km per hour he takes half time going downstream than going out in the same distance his average speed of upstream and downstream is​

Answer 1

Answer:

The speed of the boat while going upstream = (6 – 2) = 4km/hr. The speed of the boat while going upstream = (6 + 2) = 8km/hr.

Answer 2

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${\maltese \; {\underline{\underline{\textsf{\textbf{Given that :}}}}}}$

• A man can row in still water at rate of 6 km per hour if the steam flow at rate of 2 km per hour
• he takes half time going downstream than going out in the same distance        

${\maltese \; {\underline{\underline{\textsf{\textbf{To Find :}}}}}}$

• his average speed of upstream and downstream is

${\maltese \; {\underline{\underline{\textsf{\textbf{Full Solution :}}}}}}$  

• Let us assume that :

• The distance travelled by the man = x km

• Provided that :

• The speed of the boat is 6kmph

• The flow of the water is 3kmph

Henceforth :

• The relative speed downstream will be 8kmph
• The relative speed of upstream will be 4 kmph

Formulas Used :

• Formula to find the time taken :

• ${\small{\underline{\boxed{\pmb{\sf{ Time = \dfrac{Distance}{Speed} }}}}}}$  

• Formula used to find the average speed :

• ${\small{\underline{\boxed{\pmb{\sf{Average \; Speed = \dfrac{Total \; Distance}{Total \; Time} }}}}}}$  

Required Solution :

~ Total time taken to go down stream and upstream would be such that ,

${ : \implies} \tt \bigg( \dfrac{x}{8}+ \dfrac{x}{4} \bigg)$

${ : \implies} \tt \bigg( \dfrac{x}{8}+ \dfrac{2x}{8} \bigg)$

${ : \implies} \tt \bigg( \dfrac{3x}{8}\bigg)$

~ And the total distance covered will be 2x , so now let's find the average speed ,

${ : \implies} \bf Average \; speed = \dfrac{2x}{\dfrac{3x}{8} }$

${ : \implies} \bf Average \; speed = \dfrac{2x * 8}{3x }$  

${ : \implies} \bf Average \; speed = \dfrac{2 * 8}{3 }$  

${ : \implies} \bf Average \; speed = {\blue{\underline{\boxed{\pmb{\sf{ \dfrac{16}{3 }\;kmph}}}}}\star}$  

The average speed of the man to go up and down stream is  16/3 kmph

${\maltese \; {\underline{\underline{\textsf{\textbf{Therefore :}}}}}}$

• The average speed of him to go up and downstream is 16/3 kmph

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