The ratio of the speed of a motorboat to the | vedclass

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Question

(C) Let the speed of the motorboat be $36x\, km/h$ and the speed of the current be $5x\, km/h$.The speed of the boat along the current (downstream) is

Vedclass · Accepted Answer

$6\, h\, 50\, min$

Vedclass · Answer

(C) Let the speed of the motorboat be $36x\, km/h$ and the speed of the current be $5x\, km/h$.The speed of the boat along the current (downstream) is $36x + 5x = 41x\, km/h$.The time taken to travel downstream is $5\, h\, 10\, min = 5 + \frac{10}{60} = 5 + \frac{1}{6} = \frac{31}{6}\, h$.Distance covered $= 	ext{Speed} 	imes 	ext{Time} = 41x 	imes \frac{31}{6} = \frac{1271x}{6}\, km$.The speed of the boat against the current (upstream) is $36x - 5x = 31x\, km/h$.Time taken to return (upstream) $= \frac{	ext{Distance}}{	ext{Upstream Speed}} = \frac{1271x / 6}{31x} = \frac{1271}{6 	imes 31} = \frac{41}{6}\, h$.Converting $\frac{41}{6}\, h$ into hours and minutes: $\frac{41}{6} = 6\, h + \frac{5}{6} 	imes 60\, min = 6\, h\, 50\, min$.

The ratio of the speed of a motorboat to the speed of the water current is $36: 5$. The boat travels along with the current in $5\, h\, 10\, min$. How long will it take to return?

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