a woman can row upstream at 8 kmph and downstream at 10 kmph. find woman’s rate in still water and the rate of current.
To find the woman’s rate in still water and the rate of the current, we can use the concept of relative velocity.
Let’s assume the woman’s rate in still water is denoted as ‘w’ kmph and the rate of the current is denoted as ‘c’ kmph.
When the woman rows upstream (against the current), her effective speed is reduced. In this case, her speed relative to the ground is the difference between her rate in still water and the rate of the current. So, her speed upstream is (w - c) kmph.
Similarly, when the woman rows downstream (with the current), her effective speed is increased. In this case, her speed relative to the ground is the sum of her rate in still water and the rate of the current. So, her speed downstream is (w + c) kmph.
According to the given information, the woman rows upstream at a speed of 8 kmph and downstream at a speed of 10 kmph.
Therefore, we have the following equations:
(w - c) = 8
(w + c) = 10
To find the values of ‘w’ and ‘c’, we can solve these equations simultaneously.
Adding both equations, we get:
2w = 18
w = 9
Substituting the value of ‘w’ in one of the equations, we get:
(9 + c) = 10
c = 1
So, the woman’s rate in still water is 9 kmph and the rate of the current is 1 kmph.