Final answer:
To find the flow velocity, we calculate the speed of the boat using the distance and travel time, and then determine the flow velocity, which is found to be 9 km/h.
Step-by-step explanation:
The question involves solving a problem related to relative motion, specifically determining the flow velocity of water when a boat travels from city A to city B. Given the distance between the two cities is 45 km and the boat traveled 2.5 hours from city A to city B, we can use these values to calculate the flow velocity.
We know the total travel time is 2.5 hours and that the combined speed of the boat and the current allowed it to cover a distance of 45 km. Let's define the flow velocity as Vflow and the boat's velocity in still water as Vboat. Given that the speed of the boat is three times the speed of the current, we have Vboat = 3Vflow. The boat's total speed against the flow of water would be Vtotal = Vboat - Vflow.
The boat's speed can be calculated by dividing the total distance by the total time:
Vtotal = 45 km / 2.5 hours = 18 km/h
Now, substituting Vboat into the equation, we get:
18 km/h = (3Vflow) - Vflow
Solving this equation for Vflow gives us:
18 km/h = 2Vflow
Vflow = 18 km/h / 2
Vflow = 9 km/h
So, the flow velocity of the current is 9 km/h.