Question 1

Which of the following is the correct first step when solving the rational equation $$\frac{4x}{5} + \frac{3}{2} = \frac{3x}{10}$$?

Accepted Answer

Find the least common denominator (LCD) of $$5$$, $$2$$, and $$10.$$

Question 2

Solve for $$x$$: $$\frac{1}{x-2} - \frac{2}{x^2$-2x} = 1. $$Which of the following is a valid solution?

Accepted Answer

$$x = 3$$

Question 3

Which value of $$x is an $$extraneous solution to the equation $$\frac{3}{x} - \frac{x+21}{3x} = \frac{5}{3}$$?

Accepted Answer

$$x = 0$$

Question 4

If $$\frac{1}{p} + \frac{1}{q} = \frac{1}{f}$$, solve for $$f in $$terms of $$p$$ and $$q.$$

Accepted Answer

$$f = \frac{pq}{p+q}$$

Question 5

Melissa can clean a house in 4 hours, and Zack can do it in 5 hours. How long will it take them to clean the house together?

Accepted Answer

$$\frac{20}{9}$$ hours

Question 6

Given the equation $$\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$$, solve for $$x in $$terms of $$y$$ and $$z.$$

Accepted Answer

$$x = \frac{yz}{y-z}$$

Question 7

Three machines can fill a daily quota in 5 hours, 6 hours, and 7.5 hours, respectively. How long will it take all three machines working together to fill the quota?

Accepted Answer

$$1.92$$ hours

Question 8

Which of the following best describes an extraneous solution in the context of rational equations?

Accepted Answer

A solution that makes the denominator zero.

Question 9

If $$F = -\frac{GMm}{r^2$}$$, solve for $$M in $$terms of $$F$$, $$G$$, $$m$$, and $$r.$$

Accepted Answer

$$M = -\frac{Fr^2$}{Gm}$$

Question 10

A hose can fill a pond in 45 minutes. Two hoses together can fill it in 20 minutes. How long does it take the second hose alone to fill the pond?

Accepted Answer

$$60$$ minutes

Question 11

Which of the following is the correct LCD for the equation $$\frac{1}{x+3} = \frac{2}{x+3}$$?

Accepted Answer

$$x+3$$

Question 12

If $$\frac{x^2$+1}{x} = \frac{5}{x}$$, what is the value of $$x$$?

Accepted Answer

$$x = 1$$

Question 13

Chris and Mark can check all the plants in a field in 24 minutes together. Chris alone takes 36 minutes. How long does Mark take alone?

Accepted Answer

$$48$$ minutes

Question 14

Which of the following is the correct formula for the time it takes two workers to complete a task together, if their individual times are $$M_1$$ and $$M_2$$?

Accepted Answer

$$M_{together} = \frac{M_1$ M_2$}{M_1$ + M_2$}$$

Question 15

Solve for $$f_2 in $$the formula $$f = \frac{f_1$ f_2$}{f_1$ + f_2$}.$$

Accepted Answer

$$f_2$$ = \frac{f $$f_1$$}{$$f_1 - f$$}$$

Question 16

The inlet pipe of an oil tank can fill the tank in 1 hour 32 minutes. The outlet pipe can empty the tank in 1 hour. If both pipes are open, how long will it take to empty a full tank?

Accepted Answer

$$3$$ hours 4$ minutes

Question 17

Three postal workers can sort a stack of mail in 20 minutes, 30 minutes, and 60 minutes, respectively. How long will it take them to sort the mail together?

Accepted Answer

$$12$$ minutes

Solving Rational Equations and Applications in Intermediate Algebra

Study Guide - Practice Questions

Study Guide - Flashcards