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

Let's solve each problem step by step.

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Problem 1:

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

Solution:
The formula for speed is:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
Given:
- Distance = 30 miles
- Time = 4 hours

Substitute the values into the formula:
\[
\text{Speed} = \frac{30 \text{ miles}}{4 \text{ hours}} = 7.5 \text{ mph}
\]

Answer:
\[
\boxed{7.5 \text{ mph}}
\]

---

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?

Solution:
First, calculate the distance covered by the car:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
Given:
- Speed = 50 mph
- Time = 3 hours

Substitute the values:
\[
\text{Distance} = 50 \text{ mph} \times 3 \text{ hours} = 150 \text{ miles}
\]

Now, we need to find the new speed required to cover the same distance (150 miles) in 4.5 hours. Using the speed formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
Given:
- Distance = 150 miles
- Time = 4.5 hours

Substitute the values:
\[
\text{Speed} = \frac{150 \text{ miles}}{4.5 \text{ hours}} = \frac{150}{4.5} \approx 33.33 \text{ mph}
\]

Answer:
\[
\boxed{33.33 \text{ mph}}
\]

---

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?

Solution:
First, calculate the distance covered in the first part:
\[
\text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1
\]
Given:
- Speed_1 = 15 km/h
- Time_1 = 2 hours

Substitute the values:
\[
\text{Distance}_1 = 15 \text{ km/h} \times 2 \text{ hours} = 30 \text{ km}
\]

Next, calculate the distance covered in the second part. Convert 1 hour 25 minutes to hours:
\[
1 \text{ hour } 25 \text{ minutes} = 1 + \frac{25}{60} = 1 + \frac{5}{12} = \frac{12}{12} + \frac{5}{12} = \frac{17}{12} \text{ hours}
\]

Now, calculate the distance:
\[
\text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2
\]
Given:
- Speed_2 = 18 km/h
- Time_2 = \(\frac{17}{12}\) hours

Substitute the values:
\[
\text{Distance}_2 = 18 \text{ km/h} \times \frac{17}{12} \text{ hours} = \frac{18 \times 17}{12} = \frac{306}{12} = 25.5 \text{ km}
\]

Finally, add the distances from both parts:
\[
\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 30 \text{ km} + 25.5 \text{ km} = 55.5 \text{ km}
\]

Answer:
\[
\boxed{55.5 \text{ km}}
\]

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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?

Solution:
First, calculate the time taken to travel the first 40 miles:
\[
\text{Time}_1 = \frac{\text{Distance}_1}{\text{Speed}_1}
\]
Given:
- Distance_1 = 40 miles
- Speed_1 = 40 mph

Substitute the values:
\[
\text{Time}_1 = \frac{40 \text{ miles}}{40 \text{ mph}} = 1 \text{ hour}
\]

Next, calculate the time taken to travel the next 60 miles:
\[
\text{Time}_2 = \frac{\text{Distance}_2}{\text{Speed}_2}
\]
Given:
- Distance_2 = 60 miles
- Speed_2 = 50 mph

Substitute the values:
\[
\text{Time}_2 = \frac{60 \text{ miles}}{50 \text{ mph}} = 1.2 \text{ hours}
\]

Finally, add the times from both parts:
\[
\text{Total Time} = \text{Time}_1 + \text{Time}_2 = 1 \text{ hour} + 1.2 \text{ hours} = 2.2 \text{ hours}
\]

Answer:
\[
\boxed{2.2 \text{ hours}}
\]

---

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.

Solution:
Use the formula for time:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Given:
- Distance = 11 miles
- Speed = 60 mph

Substitute the values:
\[
\text{Time} = \frac{11 \text{ miles}}{60 \text{ mph}} = \frac{11}{60} \text{ hours}
\]

Convert hours to minutes (1 hour = 60 minutes):
\[
\text{Time in minutes} = \frac{11}{60} \times 60 = 11 \text{ minutes}
\]

Answer:
\[
\boxed{11 \text{ minutes}}
\]

---

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?

Solution:
First, convert the times to hours:
- 1 hour 30 minutes = \(1 + \frac{30}{60} = 1.5\) hours
- 1 hour 10 minutes = \(1 + \frac{10}{60} = 1 + \frac{1}{6} = \frac{7}{6}\) hours

Next, calculate the distance covered in the first part:
\[
\text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1
\]
Given:
- Speed_1 = 10 km/h
- Time_1 = 1.5 hours

Substitute the values:
\[
\text{Distance}_1 = 10 \text{ km/h} \times 1.5 \text{ hours} = 15 \text{ km}
\]

Now, calculate the distance covered in the second part:
\[
\text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2
\]
Given:
- Speed_2 = 20 km/h
- Time_2 = \(\frac{7}{6}\) hours

Substitute the values:
\[
\text{Distance}_2 = 20 \text{ km/h} \times \frac{7}{6} \text{ hours} = \frac{20 \times 7}{6} = \frac{140}{6} = 23.33 \text{ km}
\]

Finally, add the distances from both parts:
\[
\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 15 \text{ km} + 23.33 \text{ km} = 38.33 \text{ km}
\]

Answer:
\[
\boxed{38.33 \text{ km}}
\]

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Final Answers:

1. \(\boxed{7.5 \text{ mph}}\)
2. \(\boxed{33.33 \text{ mph}}\)
3. \(\boxed{55.5 \text{ km}}\)
4. \(\boxed{2.2 \text{ hours}}\)
5. \(\boxed{11 \text{ minutes}}\)
6. \(\boxed{38.33 \text{ km}}\)