Final answer:
Klorina's speed in still water is 4.5 km/h, as calculated by averaging the speeds with and against the current. The rate of the current is 0.5 km/h, found by solving two simple linear equations representing her speeds with and against the current.
Step-by-step explanation:
The question asks to determine Klorina's swimming speed in still water and the rate of the current. These can be calculated using the concepts of speed, distance, and time. When Klorina swims with the current, her speed increases due to the current's assistance. When she swims against the current, her speed decreases due to the current's opposition. The rate of the current will be the difference between the two speeds, and her speed in still water will be the average of the two speeds.
Let x be Klorina's speed in still water and y be the rate of the current. Swimming with the current, her effective speed is x + y, while against the current it is x - y.
With the current:
x + y = distance/time = 10 km / 2 hours = 5 km/h
Against the current:
x - y = distance/time = 8 km / 2 hours = 4 km/h
Now we have two equations:
1) x + y = 5 km/h
2) x - y = 4 km/h
By adding these two equations, we get:
x + y + x - y = 5 km/h + 4 km/h
2x = 9 km/h
x = 4.5 km/h
Substitute x back into either equation to solve for y:
Using 1) x + y = 5 km/h:
4.5 km/h + y = 5 km/h
y = 0.5 km/h
Therefore, Klorina can swim at 4.5 km/h in still water, and the current's rate is 0.5 km/h.