Instructions
Welcome to the Speed, Distance, and Time challenge! In this worksheet, you'll solve problems using the three core formulas that connect these measurements. Remember to always pay close attention to the units (like km, miles, hours, seconds).
The Three Key Formulas:
- To find Speed: Speed = Distance / Time
- To find Distance: Distance = Speed × Time
- To find Time: Time = Distance / Speed
You can use the formula triangle to help you remember! Cover the value you want to find, and the triangle shows you the calculation to do.
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S x T
Part A: The Basics
Complete the table below by calculating the missing value. Make sure your answer includes the correct units.
| Distance | Speed | Time |
|---|---|---|
| 150 km | 50 km/h | ? |
| ? | 12 m/s | 20 seconds |
| 26 miles | ? | 2 hours |
| 400 meters | 80 m/s | ? |
| ? | 70 mph | 3.5 hours |
Part B: Word Problems
Read each problem carefully and show your calculation.
- A high-speed train travels a distance of 490 km in 2 hours. What is its average speed in km/h?
- A snail is famous for its slow pace. If it moves at a speed of 0.01 meters per second, how far will it travel in 5 minutes? (Hint: First, convert minutes to seconds!)
- The International Space Station orbits Earth at a speed of about 28,000 km/h. How long does it take to travel a distance of 42,000 km?
- Sarah is training for a marathon. She runs for 2.5 hours at an average speed of 8 mph. What distance did she cover?
- A car journey of 225 miles took 4 hours and 30 minutes. What was the average speed of the car in miles per hour (mph)? (Hint: Convert the time into hours first, for example, 30 minutes is 0.5 hours).
Part C: The Challenge
Think carefully about this two-part problem!
A cyclist travels from their home to the top of a hill, a distance of 15 km. Their average speed going uphill is 10 km/h. The journey back down the same route is much faster, and their average speed is 30 km/h.
- What is the total time for the entire round trip (uphill and downhill)?
- What is the cyclist's average speed for the entire journey? (Warning: It's not the average of 10 km/h and 30 km/h!)
Answer Key
Part A: The Basics
| Distance | Speed | Time |
|---|---|---|
| 150 km | 50 km/h | 3 hours (150 / 50) |
| 240 meters (12 x 20) | 12 m/s | 20 seconds |
| 26 miles | 13 mph (26 / 2) | 2 hours |
| 400 meters | 80 m/s | 5 seconds (400 / 80) |
| 245 miles (70 x 3.5) | 70 mph | 3.5 hours |
Part B: Word Problems
- Speed = Distance / Time = 490 km / 2 hours = 245 km/h.
- Time in seconds: 5 minutes × 60 seconds/minute = 300 seconds.
Distance = Speed × Time = 0.01 m/s × 300 s = 3 meters. - Time = Distance / Speed = 42,000 km / 28,000 km/h = 1.5 hours (or 1 hour and 30 minutes).
- Distance = Speed × Time = 8 mph × 2.5 hours = 20 miles.
- Time in hours: 4 hours and 30 minutes = 4.5 hours.
Speed = Distance / Time = 225 miles / 4.5 hours = 50 mph.
Part C: The Challenge
- Time uphill: Time = Distance / Speed = 15 km / 10 km/h = 1.5 hours.
Time downhill: Time = Distance / Speed = 15 km / 30 km/h = 0.5 hours.
Total Time: 1.5 hours + 0.5 hours = 2 hours. - Total Distance: 15 km (uphill) + 15 km (downhill) = 30 km.
Total Time: 2 hours (from part 1).
Average Speed = Total Distance / Total Time = 30 km / 2 hours = 15 km/h.