A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/h and the speed of the current is 3.5 km/h, the distance between A and B is: (correct up to two decimal places)

Speed of the boat in still water = 9 km/h

Speed of the current = 3.5 km/h

Total time taken for the journey upstream and downstream = 3 hours

Concept Used: The time taken for the boat to travel a certain distance upstream and downstream can be calculated by considering the effective speed of the boat in both directions:

Upstream speed = Speed of the boat in still water - Speed of the current

Downstream speed = Speed of the boat in still water + Speed of the current

​$$\text{Time} = \frac{\text{Distance}}{\text{ Speed}}$$ 

Let the distance be AB = x km

Speed of upstream = 9-3.5 = 5.5 km/hr

Speed of downstream = 9 + 3.5 = 12.5 km/hr

ATQ,

​$$\frac{x}{12.5}+ \frac{x}{5.5} = 3$$

On solving x= 11.46 km​​