Question

When Klorina swims with the current, she swims 10 km in 2 h. Against the current, she can swim only 8 km in the same time. How fast can Klorina swim in still water? What is the rate of the current?

Answer 1

Answer:

Klorina's rate in still water is 4.5 km/h

Current's rate is 0.5 km/h

Step-by-step explanation:

Let

x km/h = Klorina's rate in still water

y km/h = current's rate

With the current (current helps):

Distance = 10 km

Time = 2 hours

Rate = x + y km/h

$10=2(x+y)$

Against the current:

Distance = 8 km

Time = 2 hours

Rate = x - y km/h

$8=2(x-y)$

Divide both equations by 2:

$x+y=5\\ \\x-y=4$

Add these equations:

$x+y+x-y=5+4\\ \\2x=9\\ \\x=4.5\ km/h$

Subtract these two equations:

$(x+y)-(x-y)=5-4\\ \\x+y-x+y=1\\ \\2y=1\\ \\y=0.5\ km/h$

Answer 2

Klorina speed in still water is 4.5 km/h and rate of the current is 0.5 km/h

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent Klorina speed in still water and b represent the rate of the current.

(a + b) = 10/2

a + b = 5    (1)

(a - b) = 8/2

a - b = 4    (2)

Solving equation 1 and 2 simultaneously gives:

a = 4.5, b = 0.5

Klorina speed in still water is 4.5 km/h and rate of the current is 0.5 km/h

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