When swimming in the direction of the current in a river your average speed is 5 mph. When swimming against the current your speed is 2mph. Find your swimming speed in still water and the speed of the current.
speed of current --- y
speed of swimming ---- x
x+y = 5
x-y = 2
solve, I suggest adding them, etc
To solve this problem, let's assume that your swimming speed in still water is represented by "S" and the speed of the current is represented by "C".
When swimming in the direction of the current, your effective speed is equal to the sum of your swimming speed and the speed of the current. So, it can be written as S + C.
Similarly, when swimming against the current, your effective speed is equal to the difference between your swimming speed and the speed of the current. So, it can be written as S - C.
Given that your average speed when swimming in the direction of the current is 5 mph, we can set up the equation:
S + C = 5
Similarly, when swimming against the current, your average speed is 2 mph, giving us another equation:
S - C = 2
To find the swimming speed in still water and the speed of the current, we can solve these two equations simultaneously.
Let's start by adding both equations together:
(S + C) + (S - C) = 5 + 2
2S = 7
Now, divide both sides of the equation by 2 to isolate S:
2S/2 = 7/2
S = 3.5 mph
So, your swimming speed in still water is 3.5 mph.
To find the speed of the current, substitute the value of S into one of the original equations:
3.5 + C = 5
Subtract 3.5 from both sides to isolate C:
C = 5 - 3.5
C = 1.5 mph
Therefore, your swimming speed in still water is 3.5 mph, and the speed of the current is 1.5 mph.