Answer:
speed of the river is 2.25 km/hr.
Step-by-step explanation:
To determine the speed of the river, we need to calculate the speed of the boat relative to still water. Let's assume the speed of the boat in still water is Vb (in km/hr), and the speed of the river is Vr (in km/hr).
When the boat travels downstream (with the direction of the river's flow), its effective speed is increased by the speed of the river. When the boat travels upstream (against the direction of the river's flow), its effective speed is decreased by the speed of the river.
Given:
Time taken to travel downstream = 3.0 hours
Time taken to travel upstream = 6.0 hours
Distance traveled in each direction = 27 km
Let's use the formula:
Speed = Distance / Time
For the downstream journey:
Vb + Vr = 27 km / 3.0 hr
Vb + Vr = 9 km/hr
For the upstream journey:
Vb - Vr = 27 km / 6.0 hr
Vb - Vr = 4.5 km/hr
Now, we have a system of equations with two variables. We can solve these equations to find the values of Vb and Vr.
Adding the two equations together, we get:
2Vb = 9 km/hr + 4.5 km/hr
2Vb = 13.5 km/hr
Vb = 13.5 km/hr / 2
Vb = 6.75 km/hr
Substituting the value of Vb back into one of the equations, we can solve for Vr:
6.75 km/hr + Vr = 9 km/hr
Vr = 9 km/hr - 6.75 km/hr
Vr = 2.25 km/hr
Therefore, the speed of the river is 2.25 km/hr.