a boat takes 3 hours 36 min more to travel 20 km upstream than 14 km downstream,if the Speed of the boat is 20 km per hour,find speed of steam
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Let, the speed of the stream be x km/hr
Speed of boat in still water =20 km/hr
∴Speed of boat with downstream 20+x km/hr
∴ Speed of boat with upstream 20−x km/hr
As per given condition
20−x
48
−
20+x
48
=1
⟹48[
20−x
1
−
20+x
1
]=1
⟹[
(20−x)(20+x)
20+x−20+x
]=
48
1
⟹
400−x
2
2x
=
48
1
⟹96x=400−x
2
⟹x
2
+96x−400=0
⟹x
2
+100x−4x−400
⟹x(x+100)−4(x+100)=0
⟹(x−4)(x+100)=0
Either, x=4 or x=−100
∵ Speed cannot be negative ∴x=4 km/hr is considered.
∴ the speed of the stream =4 km/hr
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