If the speed of a boat in still water is 10 km/hr and speed of water current is 3
km/hr, then the speed of boat upstream is _________km/hr.
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Answer:
⇒ Let x be the speed of the stream.
⇒ Speed of the boat in still water is 8km/hr
⇒ The speed of the boat in upstream is 8−xkm/hr
⇒ The speed of the boat in downstream is 8+xkm/hr
⇒ The time taken by the boat to cover 15km=
8−x
15
hr
⇒ The time taken by the boat to cover 22km=
8+x
22
hr
According to the question,
⇒
8−x
15
+
8+x
22
=5
⇒ 15(8+x)+22(8−x)=5(8−x)(8+x)
⇒ 120+15x+176−22x=5(64−x
2
)
⇒ 296−7x=320−5x
2
⇒ 5x
2
−7x−24=0
⇒ 5x
2
−15x+8x−24=0
⇒ 5x(x−3)+8(x−3)=0
⇒ (x−3)(5x+8)=0
⇒ x−3=0 and 5x+8=0
⇒ x=3 and x=−
5
8
Speed cannot be negative.
∴ The speed of the stream is 3km/hr
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