Camille can swim against the current at 1.5 m/s and with the current at 3.5m/s. Write an equation that expresses each fact. How fast can she swim in still water?
the upstream and downstream speeds differ by twice the current speed, or 2 m/s.
so, still-water speed is 2.5 m/s
up = s+r
down = s-r
s = (up+down)/2 = (1.5+3.5)/2 = 2.5
Let's assume the speed at which Camille can swim in still water is "x" m/s.
According to the problem statement, Camille can swim against the current at 1.5 m/s, which means her effective speed is her swimming speed in still water minus the speed of the current. So, the equation that expresses this fact is:
Camille's speed against the current = Camille's speed in still water - Current's speed
=> 1.5 m/s = x m/s - Current's speed (Equation 1)
Similarly, Camille can swim with the current at 3.5 m/s. In this case, her effective speed is her swimming speed in still water plus the speed of the current. So, the equation that expresses this fact is:
Camille's speed with the current = Camille's speed in still water + Current's speed
=> 3.5 m/s = x m/s + Current's speed (Equation 2)
To find out how fast Camille can swim in still water, we need to solve these two equations simultaneously.
Let's subtract Equation 1 from Equation 2 to eliminate the Current's speed:
3.5 m/s - 1.5 m/s = (x m/s + Current's speed) - (x m/s - Current's speed)
2 m/s = 2 * Current's speed
Dividing both sides of the equation by 2, we get:
Current's speed = 1 m/s
Substituting this value back into either Equation 1 or Equation 2, we can find the speed at which Camille can swim in still water.
From Equation 1:
1.5 m/s = x m/s - 1 m/s
Adding 1 m/s to both sides, we have:
2.5 m/s = x m/s
Therefore, Camille can swim in still water at a speed of 2.5 m/s.
To express the fact that Camille can swim against the current at 1.5 m/s, we can create the equation:
Camille's swimming speed in still water - Current speed = 1.5 m/s
Let's represent Camille's swimming speed in still water as 'v' and the current speed as 'c'. Therefore, the equation can be written as:
v - c = 1.5
To express the fact that Camille can swim with the current at 3.5 m/s, we can create another equation:
Camille's swimming speed in still water + Current speed = 3.5 m/s
Using the same representations, the equation becomes:
v + c = 3.5
Now, we have a system of equations:
v - c = 1.5
v + c = 3.5
To find Camille's speed in still water, we can solve this system of equations using elimination or substitution:
Adding the two equations together eliminates 'c':
(v - c) + (v + c) = 1.5 + 3.5
2v = 5
v = 2.5
Therefore, Camille can swim at a speed of 2.5 m/s in still water.