8.6 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 polynomial equation.

Front

What is the speed of the current if a person rows 5 mph in still water and takes the same time to row 4 miles upstream as 16 miles downstream?

Back

3 mph.

Front

If a swimmer can swim 11 miles downstream in the same time as 7 miles upstream, and the current is 4 mph, how do you find the swimmer's speed in still water?

Back

Let the swimmer's speed be x mph. The equation is (11/(x+4)) = (7/(x-4)). Solve for x.

Front

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

Back

If person A can complete a task in a hours and person B in b hours, their combined work rate is 1/a + 1/b = 1/t, where t is the time taken together.

Front

How long will it take for a friend to clean a park alone if you can do it in 2 hours and together it takes 1.2 hours?

Back

3 hours.

Front

What is the formula for mixing solutions of different concentrations?

Back

C1V1 + C2V2 = C3V3, where C is concentration and V is volume.

Front

How many quarts of a 75% acid solution must be mixed with 3 quarts of a 10% acid solution to make a 60% solution?

Back

10 quarts.

Front

If Farmer A can plow a field in 9 hours and together with Farmer B they take 5 hours, how long will it take Farmer B alone?

Back

11.25 hours.

Front

What is the concept of 'time taken' in work problems?

Back

Time taken refers to the duration required to complete a task, which can be calculated using rates of work.