Two boat landings are 8.0 km apart on the same bank of a stream that flows at 2.8 km/h. A motorboat makes the round trip between the two landings in 50 minutes. What is the speed of the boat relative to the water?

AH! Sorry, I didn't know it would make the site look messy. I've been working on these for a while now,and I promise I just a lot of work into them. i didn't realize I had posted so many. Sorry.

Yes, I am getting a bit frayed around the edges as well.

To find the speed of the boat relative to the water, we need to consider the speed of the stream. Let's break down the problem step by step:

1. Let's assume that the speed of the boat relative to the water is 'x' km/h.

2. Now, let's calculate the total time taken for the round trip. We know that the distance between the two boat landings is 8.0 km, and the speed of the stream is 2.8 km/h.

- The time taken to go downstream (from one landing to another) is given by the formula:
Time = Distance / Speed
Time_downstream = (8.0 km) / (x + 2.8 km/h)

- The time taken to go upstream (from one landing to another) is:
Time_upstream = (8.0 km) / (x - 2.8 km/h)

- The round trip time is given by:
Total_time = Time_downstream + Time_upstream
50 minutes = (8.0 km) / (x + 2.8 km/h) + (8.0 km) / (x - 2.8 km/h)

3. We have formed an equation, so now we need to solve it to find the value of 'x' (the speed of the boat relative to the water).

- To simplify the equation, we can multiply both sides by (x + 2.8 km/h)*(x - 2.8 km/h) to eliminate the denominators.

- After simplification, the equation becomes:
50 * (x + 2.8) * (x - 2.8) = 8.0 * (x - 2.8) + 8.0 * (x + 2.8)

4. Now, we can solve this equation for 'x'.

- Expanding and simplifying the equation:
50x^2 - 280x - 48 = 0

- Using the quadratic formula:
x = (-(-280) ± sqrt((-280)^2 - 4 * 50 * (-48))) / (2 * 50)

- Solving the equation, we find two values for 'x'.

5. Since speed cannot be negative, we discard the negative value and only consider the positive value for 'x'.

6. Finally, the positive value for 'x' is the speed of the boat relative to the water.

Note: The exact value of 'x' depends on the calculated solutions for the equation.

To summarize, the above steps outline the process to find the speed of the boat relative to the water by considering the round trip time and the distance between the boat landings.

Danielle, you should try answering the questions yourself before mass-posting on Jiskha. People don't like to answer questions that obviously haven't been put an effort into. Even if you don't know, post your work on the question.