Solving Rational Equations

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 equation.

Front

What is the formula for speed in terms of distance and time?

Back

Speed = Distance / Time.

Front

If a boat's speed in still water is 10 mph and the current's speed is 2 mph, what is the boat's speed downstream?

Back

Downstream speed = Speed in still water + Speed of current = 10 mph + 2 mph = 12 mph.

Front

If a boat's speed in still water is 10 mph and the current's speed is 2 mph, what is the boat's speed upstream?

Back

Upstream speed = Speed in still water - Speed of current = 10 mph - 2 mph = 8 mph.

Front

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

Back

Distance = Rate × Time.

Front

How do you find the time taken to travel a certain distance at a given speed?

Back

Time = Distance / Speed.

Front

What is the concept of working together in rates?

Back

When two or more people work together, their combined rate is the sum of their individual rates.

Front

If Farmer A can plow a field in 9 hours, what is his rate of work?

Back

Rate of Farmer A = 1 field / 9 hours = 1/9 fields per hour.

Front

If two farmers can plow a field together in 5 hours, what is their combined rate?

Back

Combined rate = 1 field / 5 hours = 1/5 fields per hour.