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Question

(A) Let the speed of the boat in still water be $x$ $kmph$ and the distance be $d$ $km.$Given,speed of the stream = $2$ $kmph.$Downstream speed = $(x

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) Let the speed of the boat in still water be $x$ $kmph$ and the distance be $d$ $km.$Given,speed of the stream = $2$ $kmph.$Downstream speed = $(x + 2)$ $kmph$ and upstream speed = $(x - 2)$ $kmph.$Time taken downstream = $45$ $minutes = \frac{45}{60} = \frac{3}{4}$ $hours.$Time taken upstream = $1$ $hour$ $15$ $minutes = \frac{75}{60} = \frac{5}{4}$ $hours.$Since distance is constant,$d = 	ext{speed} 	imes 	ext{time}.$$d = (x + 2) 	imes \frac{3}{4} = (x - 2) 	imes \frac{5}{4}.$Multiplying both sides by $4$,we get $3(x + 2) = 5(x - 2).$$3x + 6 = 5x - 10.$$2x = 16 \Rightarrow x = 8$ $kmph.$Thus,the speed of the boat in still water is $8$ $kmph.$

$A$ boat covered a certain distance travelling downstream in $45$ $minutes,$ while it came back to the starting point in $1$ $hour$ $15$ $minutes.$ The speed of the stream is $2$ $kmph.$ What is the speed of the boat in still water? (in $kmph$)

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