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Algebra Word Problems Practice Tests

These Grade 9 Math practice tests cover consecutive numbers, ages and averages, rates and distance, travel, money and percentages, tickets, commissions, interest, geometry, work rates, mixtures, growth, break-even models, and fixed-plus-variable costs.

Skills covered

  • Defining variables and translating words into equations
  • Solving number, average, rate, distance, and work problems
  • Modeling discounts, tax, tips, commissions, interest, tickets, and budgets
  • Using perimeter, area, volume, circles, triangles, and the Pythagorean theorem
  • Interpreting mixtures, percentages, growth, break-even points, and real-world units

How to use these practice tests

Read the question for quantities and units, define one unknown, write a relationship, solve step by step, and reject values that do not fit the situation. Include units in the final answer.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Algebra Word Problems Practice Tests

Practice Grade 9 Math questions about number problems, rates, distance, money, percentages, tickets, geometry, work, mixtures, growth, and algebraic models.

Choose the best answer. Define the unknown, write an equation or model, keep units consistent, solve, and check that the result makes sense in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A car travels 60 miles per hour for 3.5 hours. How far does it travel?

Please select an answer first.

Correct answer: A

The correct answer is 210 miles.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use distance = rate × time: 60 × 3.5 = 210 miles.
  3. Check the context: The correct choice is 210 miles.

Use distance = rate × time: 60 × 3.5 = 210 miles.

2. QuestionMultiple choice

A student walks 4 miles at 3 miles per hour. How long does the walk take?

Please select an answer first.

Correct answer: B

The correct answer is 1131\frac{1}{3} hours.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use time = distance/rate = 4/3 hours, which is 1 and 1/3 hours.
  3. Check the context: The correct choice is 1131\frac{1}{3} hours.

Use time = distance/rate = 4/3 hours, which is 1 and 1/3 hours.

3. QuestionMultiple choice

Two cars travel toward each other at 55 and 45 miles per hour. How far apart are they after 3 hours?

Please select an answer first.

Correct answer: C

The correct answer is 300 miles.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Their combined rate is 100 miles per hour, so 100 × 3 = 300 miles.
  3. Check the context: The correct choice is 300 miles.

Their combined rate is 100 miles per hour, so 100 × 3 = 300 miles.

4. QuestionMultiple choice

A cyclist rides at 12 miles per hour for 2.5 hours. What distance is covered?

Please select an answer first.

Correct answer: D

The correct answer is 30 miles.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Distance = 12 × 2.5 = 30 miles.
  3. Check the context: The correct choice is 30 miles.

Distance = 12 × 2.5 = 30 miles.

5. QuestionMultiple choice

A plane travels 400 miles at 200 miles per hour. How long is the flight without stops?

Please select an answer first.

Correct answer: A

The correct answer is 2 hours.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use time = distance/rate = 400/200 = 2 hours.
  3. Check the context: The correct choice is 2 hours.

Use time = distance/rate = 400/200 = 2 hours.

6. QuestionMultiple choice

A faster train travels 70 miles per hour and is 40 miles behind a train traveling 50 miles per hour. How long until it catches up?

Please select an answer first.

Correct answer: B

The correct answer is 2 hours.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: The relative speed is 20 miles per hour, so 40/20 = 2 hours.
  3. Check the context: The correct choice is 2 hours.

The relative speed is 20 miles per hour, so 40/20 = 2 hours.

7. QuestionMultiple choice

A boat travels downstream at 14 miles per hour for 3 hours. How far does it travel?

Please select an answer first.

Correct answer: C

The correct answer is 42 miles.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Distance = rate × time = 14 × 3 = 42 miles.
  3. Check the context: The correct choice is 42 miles.

Distance = rate × time = 14 × 3 = 42 miles.

8. QuestionMultiple choice

A driver travels 120 miles in 2.5 hours. What is the average speed?

Please select an answer first.

Correct answer: D

The correct answer is 48 miles per hour.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Average speed = distance/time = 120/2.5 = 48 miles per hour.
  3. Check the context: The correct choice is 48 miles per hour.

Average speed = distance/time = 120/2.5 = 48 miles per hour.

9. QuestionMultiple choice

A distance model is d=80td=80t. How far does an object travel in 4.5 time units?

Please select an answer first.

Correct answer: A

The correct answer is 360 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Substitute t = 4.5: d = 80(4.5) = 360.
  3. Check the context: The correct choice is 360 units.

Substitute t = 4.5: d = 80(4.5) = 360.

10. QuestionMultiple choice

A runner travels 150 meters in 3 minutes. What is the average rate?

Please select an answer first.

Correct answer: B

The correct answer is 50 meters per minute.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Average rate = 150/3 = 50 meters per minute.
  3. Check the context: The correct choice is 50 meters per minute.

Average rate = 150/3 = 50 meters per minute.

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