Speed, Time, and Distance Word Problems Worksheet | Grade1to6 - Free Printable

Let's solve each of the Speed, Time, and Distance word problems step by step. We'll use the basic formula:

> Speed = Distance ÷ Time
> Distance = Speed × Time
> Time = Distance ÷ Speed

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Problem 1:

A cyclist covers a distance of 30 miles in 4 hours. Calculate his speed.

- Given:
- Distance = 30 miles
- Time = 4 hours

$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{30}{4} = 7.5 \text{ mph}
$$

✔ Answer: 7.5 miles per hour (mph)

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Problem 2:

A car takes 3 hours to cover a distance, if it travels at a speed of 50 mph. What should be its speed to cover the same distance in 4.5 hours?

- First, find the distance:
- Speed = 50 mph
- Time = 3 hours
$$
\text{Distance} = 50 \times 3 = 150 \text{ miles}
$$

- Now, find new speed to cover 150 miles in 4.5 hours:
$$
\text{Speed} = \frac{150}{4.5} = 33.\overline{3} \approx 33.33 \text{ mph}
$$

✔ Answer: 33.33 mph (or $ \frac{100}{3} $ mph)

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Problem 3:

Bill roller skates for 2 hours with a constant speed of 15 km/h and then for another 1 hour 25 minutes with a constant speed of 18 km/h. What distance did he go?

- First part:
- Time = 2 hours
- Speed = 15 km/h
$$
\text{Distance}_1 = 15 \times 2 = 30 \text{ km}
$$

- Second part:
- Time = 1 hour 25 minutes = $ 1 + \frac{25}{60} = 1 + \frac{5}{12} = \frac{17}{12} $ hours
- Speed = 18 km/h
$$
\text{Distance}_2 = 18 \times \frac{17}{12} = \frac{306}{12} = 25.5 \text{ km}
$$

- Total distance:
$$
30 + 25.5 = 55.5 \text{ km}
$$

✔ Answer: 55.5 km

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Problem 4:

A train travels 40 miles with a constant speed of 40 mph and another 60 miles with a constant speed of 50 mph. How much time in total does it take to travel these distances?

- First part:
- Distance = 40 miles
- Speed = 40 mph
$$
\text{Time}_1 = \frac{40}{40} = 1 \text{ hour}
$$

- Second part:
- Distance = 60 miles
- Speed = 50 mph
$$
\text{Time}_2 = \frac{60}{50} = 1.2 \text{ hours} = 1 \text{ hour } 12 \text{ minutes}
$$

- Total time:
$$
1 + 1.2 = 2.2 \text{ hours} = 2 \text{ hours } 12 \text{ minutes}
$$

✔ Answer: 2 hours 12 minutes

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Problem 5:

A car travels at an average speed of 60 mph. How long will it take for the car to travel 11 miles? Give your answer in minutes.

- Speed = 60 mph
- Distance = 11 miles
$$
\text{Time} = \frac{11}{60} \text{ hours}
$$

Convert to minutes:
$$
\frac{11}{60} \times 60 = 11 \text{ minutes}
$$

✔ Answer: 11 minutes

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Problem 6:

Rodney rides his bike for 1 hour 30 minutes with a constant speed of 10 km/h and then for another 1 hour 10 minutes with a constant speed of 20 km/h. What distance did he go?

- First part:
- Time = 1 hour 30 minutes = 1.5 hours
- Speed = 10 km/h
$$
\text{Distance}_1 = 10 \times 1.5 = 15 \text{ km}
$$

- Second part:
- Time = 1 hour 10 minutes = $ 1 + \frac{10}{60} = 1 + \frac{1}{6} = \frac{7}{6} $ hours
- Speed = 20 km/h
$$
\text{Distance}_2 = 20 \times \frac{7}{6} = \frac{140}{6} \approx 23.33 \text{ km}
$$

- Total distance:
$$
15 + 23.33 = 38.33 \text{ km}
$$

✔ Answer: 38.33 km (or $ \frac{115}{3} $ km)

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 7.5 mph |
| 2 | 33.33 mph |
| 3 | 55.5 km |
| 4 | 2 hours 12 minutes |
| 5 | 11 minutes |
| 6 | 38.33 km |

Let me know if you'd like this as a printable solution sheet!