Final answer:
To find Karen's speed in still water, we can set up a system of equations based on the given information and solve them to find the value of x.
Step-by-step explanation:
To find Karen's speed in still water, we can set up a system of equations based on the given information.
Let's assume that Karen's speed in still water is represented by x mph.
When Karen is rowing downstream, her effective speed is the sum of her rowing speed and the current's speed, which is (x + 2) mph.
Similarly, when she is rowing upstream, her effective speed is the difference between her rowing speed and the current's speed, which is (x - 2) mph.
We are given that the distance downstream is 63 miles and the return trip upstream took 12 hours longer. Using the formula Distance = Speed × Time, we can set up the following equations:
Equation 1: 63 = (x + 2) × t
Equation 2: 63 = (x - 2) × (t + 12)
Solving these equations simultaneously will give us the value of x, the speed of Karen in still water.
Let's solve Equation 1 for t:
t = 63 / (x + 2)
Substitute this value of t into Equation 2:
63 = (x - 2) × (63 / (x + 2) + 12)
Now, we can solve this equation to find x, Karen's speed in still water.