Solving Water Current Speed Problems Using Algebra

When tackling problems related to water current speed, it's essential to understand the relationship between the boat's speed in still water, the speed of the stream, and the resulting downstream and upstream speeds. This article will guide you through a detailed algebraic solution to a specific problem involving Akansha rowing a boat in both directions. Understanding these concepts can help in effectively solving similar problems and optimizing SEO for search engine queries related to these topics.

Understanding the Problem

The problem at hand involves Akansha rowing a boat with a given speed in both upstream and downstream directions. Here's the problem statement: Akansha can row upstream at 24 km/h and downstream at 16 km/h. The task is to determine the speed of the stream.

Formulating the Equations

To solve this problem, let's define two variables:

Let the speed of the boat in stillwater be x km/h.

Let the speed of the stream be y km/h.

The speed of the boat in the upstream direction is deduced from the fact that the stream reduces the boat's speed, resulting in x - y. Given:

x - y 24

The speed of the boat in the downstream direction, where the stream adds to the boat's speed, is represented by x y. Given:

x y 16

Solving the Equations

To find the values of x and y, we need to solve these two equations simultaneously:

x - y 24 x y 16

Adding these two equations together:

2x 40

Dividing by 2:

x 20

Now that we have x, we can substitute it back into one of the original equations to find y. Using the first equation:

20 - y 24

Solving for y:

y -4

The negative value of y indicates that the stream is against the direction of the boat in the upstream scenario, which is consistent with the problem statement.

Conclusion

The speed of the boat in stillwater is 20 km/h, and the speed of the stream is -4 km/h. It's important to note that the speed of the stream is a positive value when considering its downstream impact, thus, |y| 4 km/h.

SEO Optimization and Keyword Integration

For effective SEO optimization, the following keywords should be integrated throughout the content:

boat speed stream speed algebraic equations downstream speed upstream speed

By incorporating these keywords in a natural and coherent manner, the article will rank well in search engine results for relevant queries related to water current speed problems and algebra.

Example Link: Water Current Speed Problems