Quiz 2 Operations with Rational Relationships

Driving to her summer cottage, Rachel averaged 80 mph. Since the weather was so good she decided to ride her bike back to town and was able to average 20 mph. If the total time for the round trip is 8 hours, then how far is it from the cottage to town?

• 102 miles

• 112 miles

• 120 miles

• 128 miles

Leanne takes 3 hours to do a job and Julie takes 4 hours to do the same job. If they work together, how many hours will it take them to complete the job?

• 2/7 hours

• 7/12 hours

• 12/7 hours

• 12/5 hours

Amy takes 5 hours to do a job. If Chandler helps her they complete the job in 3 hours. How many hours would it take Chandler to do the same job is he were working alone?

• 2/15

• 15/8

• 15/7

• 15/2

Mark solved the following rational equation and found solutions of 2 and 5. Which of the following statements is TRUE?

• 2 and 5 are both real solutions.

• 2 and 5 are both extraneous solutions.

• 2 is a real solution, but 5 is an extraneous solution.

• 5 is a real solution, but 2 is an extraneous solution.

Julie solved the following rational equation and found solutions of 1 and 4. Which of the following statement is TRUE?

• 1 and 4 are both real solutions.

• 1 and 4 are both extraneous solutions.

• 1 is a real solution, but 4 is an extraneous solution.

• 4 is a real solution, but 1 is an extraneous solution.

How many real solutions does the following equation have?

• 0

• 1

• 2

• Infinitely Many

Given the following equation, for what values of x is the equation true?

• no real values of x

• all real values of x

• all real values of x except 3

• x = 3 only

Solve.

• -7, 2

• -1, 14

• -2, 7

• -14, 1

Find the solution set for the following equation.

• 5

• -2.5

• -2.5, 5

• There is no solution.

Emily, Brad, Chad, and David carpool to work every weekday morning. The fuel efficiency of Brad's car is m miles per gallon driving in the city. Their commute to work is 20 miles on the highway and 8 miles in the city. The total amount of gas consumed driving to work in Brad's car is given by the following expression. What is the meaning of the term 8/m-4 in the context of the problem?

• The amount of gas consumed driving on the highway.

• The total amount of gas consumed driving to work.

• The amount of gas consumed driving in the city.

• The number of miles driven in the city.