The speed of a stream is 9 km/h.
The speed of a stream is 9 km/h. A boat can go 56 km downstream and 28 km upstream in 7 hours. What is the speed (in km/h) of the boat in still water?
एक धारा की चाल 9 km/h है। एक नाव धारा के अनुकूल 56 km और धारा के प्रतिकूल 28 km की दूरी 7 घंटे में तय कर सकती है। स्थिर जल में नाव की चाल (km/h में) ज्ञात कीजिए।
Detailed Solution & Logic
15
Let the speed of the boat in still water be $ x $ km/h
Speed of stream = $ 9 \text{ km/h} $
Downstream speed = $ x+9 $
Upstream speed = $ x-9 $
Total time = 7 hours
$ \frac{56}{x+9} + \frac{28}{x-9} = 7 $
$ 56(x-9) + 28(x+9) = 7(x^2 - 81) $
$ 56x - 504 + 28x + 252 = 7x^2 - 567 $
$ 84x - 252 = 7x^2 - 567 $
$ 7x^2 - 84x - 315 = 0 $
$ x^2 - 12x - 45 = 0 $
$ (x-15)(x+3)=0 $
$ x = 15 $ km/h
Answer: 15 km/h
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