A motorboat whose speed in 24 km per hour in still water takes 1 hour more to go 32 km upstream and return back to the same point in 4 hours 30 minutes find the speed of the stream
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Answer:
Speed of the stream = 8 km per hour
Step-by-step explanation:
The speed of the motorboat = 24 km per hour
distance = 32 km
Let the speed of the stream be 'x'
Speed of boat upstream is 24 - x
Speed of boat downstream is 24 + x
⇒ [(32/24-x) - (32/24+x)] = 1
⇒ [ 32(24+x) - 32(24-x)]/(24-x)(24+x) = 1
⇒ [768 + 32x - 768 + 32x]/576 - x² = 1
⇒ 64x = 576 - x²
⇒ x² + 64x - 576 = 0
⇒ x² - 8x + 72x - 576 = 0
⇒ x(x - 8) + 72(x - 8) = 0
⇒ (x -8)(x + 72) = 0
⇒ x = 8 or -72
⇒ x = 8 [∵ Speed cannot be a negative value]
Therefore, the speed of the stream is 8 km per hour.
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