Mr. Yogesh takes 10 hours to travel 40 km downstream and return to the same time :
spot. The speed of boat in still water is 8 km/hr. Find the speed of water current
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Answer:
Step-by-step explanation:
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The speed of water current is 0.32 km/hr.
Step-by-step explanation:
Speed of water current is taken as X km/hr
Case 1:
Speed of boat downstream = (8 + X) km/hr
Time taken to cover 40 km downstream (T₁) = [40/(8+x)] hr
Case 2:
Speed of boat upstream = (8 - x) km/hr
Time taken to cover 40km upstream (T₂) = [40/(8-x)] hr
Total time taken to go upstream and downstream = T₁ + T₂
= [40/(8+x)] + [40/(8-x)]
= [40(8-x) + 40(8+x)] / (8² - x²)
= [320 - 40x + 320 + 40x] / [64 - x²]
= 640 / (64 - x²)
Given that total time is 10 hours, so T₁ + T₂ = 10
We get 640 / (64 - x²) = 10
10 (64 - x²) = 640
640 - 10x² = 640
10x² = 1
x² =1/10 = 0.1
Therefore x = ±√0.1 = 0.32
Speed of water current = 0.32 km/hr
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