Briana can row 4 miles per hour is still water. It takes as long to row 8 miles upstream as 24 miles downstream. How fast is the current?

speed of current = u

speed upstream = (u-4)
speed downstream = (u+4)

8 = (u-4) T so T = 8/(u-4)
24 = (u+4) T so T = 24/(u+4)

8/(u-4) = 24/(u+4)

24(u-4) = 8 (u+4)

24 u - 96 = 8 u + 32

16 u = 128

u = 8

How did you do 8/(u-4) which turned in to 8(u-4)

Cross multiplication

8 24
______ = ______

u-4 u+4

8(u+4) = 24(u-4)
8u + 32 = 24u - 96
8u = 24u - 128
-16u = -128
u = 8

To determine the speed of the current, let's break down the information given:

1. Briana's speed in still water is 4 miles per hour.
2. The time it takes for her to row 8 miles upstream is the same as the time it takes for her to row 24 miles downstream.

To find the speed of the current, we need to use the concept of relative speeds.

Let's assume the speed of the current is "c" miles per hour. When Briana is rowing upstream, she is rowing against the current, so her effective speed is reduced. Similarly, when she rows downstream, she benefits from the assistance of the current, so her effective speed increases.

Let's calculate the time it takes for Briana to row upstream and downstream:

Time taken to row upstream = Distance / (Speed in still water - Speed of current)
Time taken to row downstream = Distance / (Speed in still water + Speed of current)

Using the given information, we can set up the following equations:

8 / (4 - c) = 24 / (4 + c)

We can solve this equation to find the value of "c":

8(4 + c) = 24(4 - c)
32 + 8c = 96 - 24c
32c = 64
c = 64 / 32
c = 2

Therefore, the speed of the current is 2 miles per hour.

To summarize, to find the speed of the current, we used the concept of relative speeds and set up equations based on the given information. By solving the equations, we determined that the speed of the current is 2 miles per hour.