Speed of a motorboat in still water is 45 tex | vedclass

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Question

(C) Let the speed of the motorboat in still water be $u = 45 	ext{ km/h}$ and the speed of the stream be $v 	ext{ km/h}$.Time taken to travel $80

Vedclass · Accepted Answer

$2 	ext{ h } 40 	ext{ min}$

Vedclass · Answer

(C) Let the speed of the motorboat in still water be $u = 45 	ext{ km/h}$ and the speed of the stream be $v 	ext{ km/h}$.Time taken to travel $80 	ext{ km}$ along the stream (downstream) is $1 	ext{ h } 20 	ext{ min} = 1 + \frac{20}{60} 	ext{ h} = 1 + \frac{1}{3} 	ext{ h} = \frac{4}{3} 	ext{ h}$.Downstream speed $= u + v = \frac{	ext{Distance}}{	ext{Time}} = \frac{80}{4/3} = 80 	imes \frac{3}{4} = 60 	ext{ km/h}$.Since $u = 45 	ext{ km/h}$,we have $45 + v = 60$,which gives $v = 15 	ext{ km/h}$.Now,the speed against the stream (upstream) is $u - v = 45 - 15 = 30 	ext{ km/h}$.Time taken to cover $80 	ext{ km}$ upstream $= \frac{	ext{Distance}}{	ext{Upstream Speed}} = \frac{80}{30} 	ext{ h} = \frac{8}{3} 	ext{ h}$.Converting to hours and minutes: $\frac{8}{3} 	ext{ h} = 2 \frac{2}{3} 	ext{ h} = 2 	ext{ h } + (\frac{2}{3} 	imes 60) 	ext{ min} = 2 	ext{ h } 40 	ext{ min}$.

Speed of a motorboat in still water is $45 \text{ km/h}$. If the motorboat travels $80 \text{ km}$ along the stream in $1 \text{ h } 20 \text{ min}$,then the time taken by it to cover the same distance against the stream will be:

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