Bill swam
4
kilometers against the current in the same amount of time it took him to swim
12
kilometers with the current. The rate of the current was
2
kilometers per hour. How fast would Bill swim if there were no current?
since time = distance/speed,
4/(x-2) = 12/(x+2)
Now just find x.
To solve this problem, we can set up a system of equations.
Let's assume that Bill's swimming speed in still water is "x" kilometers per hour.
Against the current: Bill's speed = x - 2 (since the current is against him)
With the current: Bill's speed = x + 2 (since the current is aiding him)
Given that Bill swam 4 kilometers against the current in the same time it took him to swim 12 kilometers with the current, we can set up the following equation:
4 / (x - 2) = 12 / (x + 2)
To solve this equation, we can cross-multiply:
4(x + 2) = 12(x - 2)
Now, let's simplify and solve for x:
4x + 8 = 12x - 24
8 + 24 = 12x - 4x
32 = 8x
x = 32 / 8
x = 4
Therefore, Bill would swim at a speed of 4 kilometers per hour if there were no current.
To find out how fast Bill would swim without any current, we need to determine his swimming speed independent of the current.
Let's denote Bill's speed, or rate of swimming without any current, as x kilometers per hour.
We are given that Bill swam 4 kilometers against the current and 12 kilometers with the current in the same amount of time. We know the rate of the current is 2 kilometers per hour.
When Bill swims against the current, his effective speed is reduced by the rate of the current. So, when Bill swims against the current, his effective swimming speed is x - 2 kilometers per hour.
Similarly, when Bill swims with the current, his effective swimming speed increases by the rate of the current. So, when Bill swims with the current, his effective swimming speed is x + 2 kilometers per hour.
We can set up a proportion using the distances travelled and the effective speeds:
4 / (x - 2) = 12 / (x + 2)
To solve this proportion, we can cross-multiply:
4(x + 2) = 12(x - 2)
Expanding the equation:
4x + 8 = 12x - 24
Rearranging the equation:
12x - 4x = 8 + 24
8x = 32
Dividing both sides by 8:
x = 4
Therefore, Bill would swim at a speed of 4 kilometers per hour without any current.