Speed, Distance, and Time Math Worksheet for 13-Year-Olds

Instructions

1. Use the formulas below to solve each problem.
2. Show your work, including the numbers you substitute into the formula.
3. Write every answer with the correct unit, such as kilometers, hours, or meters per second.
4. Check that your answer is reasonable before moving on.

Formula guide

• Speed = Distance ÷ Time
• Distance = Speed × Time
• Time = Distance ÷ Speed

Helpful reminder: Convert units when needed. For example, 30 minutes = 0.5 hour, and 90 minutes = 1.5 hours.

Section 1: Choose the Correct Formula

Write S for speed, D for distance, or T for time.

1. A car travels 240 kilometers in 3 hours. Which quantity can you find? __

2. A runner travels at 8 meters per second for 20 seconds. Which quantity can you find? __

3. A train travels 360 miles at 60 miles per hour. Which quantity can you find? __

Section 2: Solve the Problems

Show your formula, substitution, calculation, and answer.

Example: A cyclist travels 30 kilometers in 2 hours. What is the cyclist’s speed?

• Formula: Speed = Distance ÷ Time
• Substitution: Speed = 30 ÷ 2
• Answer: 15 kilometers per hour

1. School bus trip: A school bus travels 150 kilometers in 3 hours. What is its average speed?

   Work: ____

   Answer: __

2. Walking challenge: Maya walks at a speed of 5 kilometers per hour for 2.5 hours. How far does she walk?

   Work: ____

   Answer: __

3. Road trip: A family drives 84 miles at an average speed of 7 miles per hour. How long does the trip take?

   Work: ____

   Answer: __

4. Robot race: A robot moves at 18 meters per second for 45 seconds. How far does it travel?

   Work: ____

   Answer: __

5. Train journey: A train travels 240 kilometers at a speed of 80 kilometers per hour. How long is the journey?

   Work: ____

   Answer: __

6. Bike ride: Jordan rides 15 kilometers in 50 minutes. What is Jordan’s average speed in kilometers per hour?

   Hint: First convert 50 minutes to hours.

   Work: ____

   Answer: __

Section 3: Compare and Reason

7. Two cyclists are traveling on different routes.

   • Cyclist A travels 48 kilometers in 2 hours.
   • Cyclist B travels 30 kilometers in 1.5 hours.

   a. Find the average speed of each cyclist.

   Cyclist A: __

   Cyclist B: __

   b. Which cyclist is traveling faster? Explain how you know.

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8. A two-part trip: A car travels 72 kilometers. During the first hour, it travels at 36 kilometers per hour. For the rest of the trip, it travels at 18 kilometers per hour.

   a. How far does the car travel during the first hour?

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   b. How far remains after the first hour?

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   c. How long does the remaining part of the trip take?

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   d. What is the total travel time?

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Section 4: Real-World Challenge

9. A delivery driver travels 120 kilometers in 2 hours and then travels another 80 kilometers in 1 hour.

   a. What total distance does the driver travel?

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   b. What total time does the driver spend traveling?

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   c. What is the driver’s average speed for the entire trip?

   Hint: Average speed = Total distance ÷ Total time.

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Optional Extension

10. A runner completes a 400-meter track in 80 seconds. At the same speed, how far will the runner travel in 3 minutes?

    Hint: Convert 3 minutes to seconds before calculating.

    Work: ____

    Answer: __

Answer Key

Section 1

1. S — Speed
2. D — Distance
3. T — Time

Section 2

1. Speed = Distance ÷ Time = 150 ÷ 3 = 50 kilometers per hour
2. Distance = Speed × Time = 5 × 2.5 = 12.5 kilometers
3. Time = Distance ÷ Speed = 84 ÷ 7 = 12 hours
4. Distance = Speed × Time = 18 × 45 = 810 meters
5. Time = Distance ÷ Speed = 240 ÷ 80 = 3 hours
6. 50 minutes = 50 ÷ 60 = 0.833 hour. Speed = 15 ÷ 0.833, or 15 × 60 ÷ 50 = 18 kilometers per hour

Section 3

7. a. Cyclist A: 48 ÷ 2 = 24 kilometers per hour. Cyclist B: 30 ÷ 1.5 = 20 kilometers per hour.

   b. Cyclist A is traveling faster because 24 kilometers per hour is greater than 20 kilometers per hour.

8. a. First hour: 36 × 1 = 36 kilometers

   b. Remaining distance: 72 − 36 = 36 kilometers

   c. Remaining time: 36 ÷ 18 = 2 hours

   d. Total time: 1 + 2 = 3 hours

Section 4

9. a. Total distance: 120 + 80 = 200 kilometers

   b. Total time: 2 + 1 = 3 hours

   c. Average speed: 200 ÷ 3 = 66⅔ kilometers per hour, or approximately 66.7 kilometers per hour

Optional Extension

10. 3 minutes = 180 seconds. Speed = 400 ÷ 80 = 5 meters per second. Distance = 5 × 180 = 900 meters