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+1 vote
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in Distance, Time and Speed by (49.3k points)
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A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be 12 km/hr, what is the distance between A and B? 

(a) 100 km 

(b) 90 km 

(c) 110 km 

(d) 120 km

1 Answer

+2 votes
by (46.3k points)
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Best answer

(b) 90 km

Speed downstream = (12 + 3) km/hr = 15 km/hr 

Speed upstream = (12 – 3) km/hr = 9 km/hr 

Let the distance between A and B be x km. Then

\(\frac{x}{15}+\frac{\frac{x}{2}}{9}=11⇒\frac{x}{15}+\frac{x}{18}=11\)

⇒ \(\frac{6x+5x}{90}=11⇒\frac{11x}{90}=11⇒x=90\) km.

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