2023 - 2024 - Rational Equations and Applications

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

Front

What is the formula for distance when considering speed and time?

Back

The formula for distance is: Distance = Speed × Time.

Front

What is the relationship between speed, distance, and time?

Back

Speed is the rate at which distance is covered over time. If you know any two of these variables, you can find the third.

Front

How do you set up an equation for a boat traveling downstream and upstream?

Back

Let x be the speed of the boat in still water. The downstream speed is (x + current speed) and the upstream speed is (x - current speed). Use the formula: Distance = Speed × Time.

Front

What is the significance of the current in river problems?

Back

The current affects the effective speed of the boat or plane, increasing it when going downstream and decreasing it when going upstream.

Front

How do you find the time taken for two people working together?

Back

If one person takes t hours to complete a job, their rate is 1/t. For two people, add their rates: Rate1 + Rate2 = Combined Rate.

Front

What is the formula for work done when two people work together?

Back

Front

How do you express the speed of a plane with wind?

Back

If the speed of the plane in still air is p and the wind speed is w, then the effective speed with the wind is (p + w) and against the wind is (p - w).

Front

What is the first step in solving a rational equation?

Back

The first step is to identify the least common denominator (LCD) of all the fractions involved.