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

Here are the step-by-step solutions for the problems on the worksheet.

1. A cyclist covers a distance of 30 miles in 4 hours. Calculate his speed.
* Step 1: Identify the formula: Speed = Distance ÷ Time.
* Step 2: Plug in the numbers: $30 \text{ miles} \div 4 \text{ hours}$.
* Step 3: Calculate: $30 \div 4 = 7.5$.
* Answer: The speed is 7.5 mph.

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?
* Step 1: First, find the total distance using the first trip's information.
* Formula: Distance = Speed × Time.
* Calculation: $50 \text{ mph} \times 3 \text{ hours} = 150 \text{ miles}$.
* Step 2: Now, calculate the new speed needed to cover that 150 miles in 4.5 hours.
* Formula: Speed = Distance ÷ Time.
* Calculation: $150 \div 4.5$.
* To make it easier, multiply both by 10: $1500 \div 45$.
* Simplify by dividing by 15: $100 \div 3 = 33.33...$
* Answer: The speed should be 33.33 mph (or $33 \frac{1}{3}$ mph).

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?
* Step 1: Calculate the distance for the first part.
* $15 \text{ km/h} \times 2 \text{ hours} = 30 \text{ km}$.
* Step 2: Convert the time for the second part into hours.
* 25 minutes is $\frac{25}{60}$ of an hour. Simplified, this is $\frac{5}{12}$ hours.
* So, the time is $1 \frac{5}{12}$ hours (or $\frac{17}{12}$ hours).
* Step 3: Calculate the distance for the second part.
* $18 \text{ km/h} \times \frac{17}{12} \text{ hours}$.
* $18 \div 12 = 1.5$.
* $1.5 \times 17 = 25.5 \text{ km}$.
* Step 4: Add the two distances together.
* $30 \text{ km} + 25.5 \text{ km} = 55.5 \text{ km}$.
* Answer: He went a total of 55.5 km.

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?
* Step 1: Calculate the time for the first part.
* Formula: Time = Distance ÷ Speed.
* $40 \text{ miles} \div 40 \text{ mph} = 1 \text{ hour}$.
* Step 2: Calculate the time for the second part.
* $60 \text{ miles} \div 50 \text{ mph} = 1.2 \text{ hours}$.
* Step 3: Convert 0.2 hours into minutes to make it clearer (optional but helpful).
* $0.2 \times 60 \text{ minutes} = 12 \text{ minutes}$.
* So, the second part took 1 hour and 12 minutes.
* Step 4: Add the times together.
* $1 \text{ hour} + 1.2 \text{ hours} = 2.2 \text{ hours}$.
* Answer: It takes 2.2 hours (or 2 hours and 12 minutes).

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.
* Step 1: Calculate the time in hours.
* Formula: Time = Distance ÷ Speed.
* $11 \div 60$ hours.
* Step 2: Convert hours to minutes.
* Since there are 60 minutes in an hour, multiply the result by 60.
* $(\frac{11}{60}) \times 60 = 11$.
* Answer: It will take 11 minutes.

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?
* Step 1: Calculate the distance for the first part.
* Convert 1 hour 30 minutes to hours: 1.5 hours.
* $10 \text{ km/h} \times 1.5 \text{ hours} = 15 \text{ km}$.
* Step 2: Calculate the distance for the second part.
* Convert 1 hour 10 minutes to hours: 10 minutes is $\frac{10}{60}$ or $\frac{1}{6}$ of an hour. So the time is $1 \frac{1}{6}$ hours (or $\frac{7}{6}$ hours).
* $20 \text{ km/h} \times \frac{7}{6} \text{ hours} = \frac{140}{6} \text{ km}$.
* $\frac{140}{6} = 23.33... \text{ km}$ (or $23 \frac{1}{3}$ km).
* Step 3: Add the two distances together.
* $15 + 23.33... = 38.33...$
* Answer: He went a total of 38.33 km (or $38 \frac{1}{3}$ km).

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Final Answer:
1. 7.5 mph
2. 33.33 mph (or $33 \frac{1}{3}$ mph)
3. 55.5 km
4. 2.2 hours (or 2 hours 12 minutes)
5. 11 minutes
6. 38.33 km (or $38 \frac{1}{3}$ km)