Distance Speed Time (A) Worksheet | Cazoom Maths Worksheets - Free Printable

Problem Analysis:

The worksheet involves two main sections:
1. Section A: Converting times given as decimals and fractions into hours and minutes.
2. Section B: Calculating average speed using the formula:
\[
\text{Average Speed} = \frac{\text{Distance Travelled}}{\text{Time Taken}}
\]
and solving for missing values when either distance or time is unknown.

Let's solve each section step by step.

---

Section A: Converting Times

#### Step 1: Understand the Conversion
- 1 hour = 60 minutes
- To convert a decimal or fraction of an hour into minutes, multiply the fractional part by 60.

#### Step 2: Solve Each Row

1. 1.5 hours
- The integer part is 1 hour.
- The fractional part is \(0.5\) hours.
- Convert \(0.5\) hours to minutes: \(0.5 \times 60 = 30\) minutes.
- Result: 1 hour 30 minutes

2. \(2 \frac{1}{4}\) hours
- The integer part is 2 hours.
- The fractional part is \(\frac{1}{4}\) hours.
- Convert \(\frac{1}{4}\) hours to minutes: \(\frac{1}{4} \times 60 = 15\) minutes.
- Result: 2 hours 15 minutes

3. 5.75 hours
- The integer part is 5 hours.
- The fractional part is \(0.75\) hours.
- Convert \(0.75\) hours to minutes: \(0.75 \times 60 = 45\) minutes.
- Result: 5 hours 45 minutes

4. 3.1 hours
- The integer part is 3 hours.
- The fractional part is \(0.1\) hours.
- Convert \(0.1\) hours to minutes: \(0.1 \times 60 = 6\) minutes.
- Result: 3 hours 6 minutes

5. \(4 \frac{2}{5}\) hours
- The integer part is 4 hours.
- The fractional part is \(\frac{2}{5}\) hours.
- Convert \(\frac{2}{5}\) hours to minutes: \(\frac{2}{5} \times 60 = 24\) minutes.
- Result: 4 hours 24 minutes

#### Final Answer for Section A:
\[
\begin{array}{|c|c|}
\hline
\text{Time} & \text{Time in hours and minutes} \\
\hline
1.5 \text{ hours} & 1 \text{ hour } 30 \text{ mins} \\
2 \frac{1}{4} \text{ hours} & 2 \text{ hours } 15 \text{ mins} \\
5.75 \text{ hours} & 5 \text{ hours } 45 \text{ mins} \\
3.1 \text{ hours} & 3 \text{ hours } 6 \text{ mins} \\
4 \frac{2}{5} \text{ hours} & 4 \text{ hours } 24 \text{ mins} \\
\hline
\end{array}
\]

---

Section B: Completing the Tables

#### Part 1: Calculate Average Speed

The formula for average speed is:
\[
\text{Average Speed} = \frac{\text{Distance Travelled}}{\text{Time Taken}}
\]

1. 140 km in 2 hours
\[
\text{Average Speed} = \frac{140 \text{ km}}{2 \text{ hours}} = 70 \text{ km/h}
\]

2. 93 miles in 3 hours
\[
\text{Average Speed} = \frac{93 \text{ miles}}{3 \text{ hours}} = 31 \text{ mph}
\]

3. 85 m in 20 seconds
\[
\text{Average Speed} = \frac{85 \text{ m}}{20 \text{ s}} = 4.25 \text{ m/s}
\]

4. 6140 miles in 8 hours
\[
\text{Average Speed} = \frac{6140 \text{ miles}}{8 \text{ hours}} = 767.5 \text{ mph}
\]

#### Part 2: Solve for Missing Values

The formula for distance is:
\[
\text{Distance Travelled} = \text{Average Speed} \times \text{Time Taken}
\]

1. Time Taken = 1 hour, Average Speed = 50 km/h
\[
\text{Distance Travelled} = 50 \text{ km/h} \times 1 \text{ hour} = 50 \text{ km}
\]

2. Time Taken = 4 hours, Average Speed = 100 mph
\[
\text{Distance Travelled} = 100 \text{ mph} \times 4 \text{ hours} = 400 \text{ miles}
\]

3. Time Taken = 30 seconds, Average Speed = 7.6 m/s
\[
\text{Distance Travelled} = 7.6 \text{ m/s} \times 30 \text{ s} = 228 \text{ m}
\]

4. Time Taken = 2 hours 30 minutes, Average Speed = 750 km/h
- Convert 2 hours 30 minutes to hours: \(2 + \frac{30}{60} = 2.5\) hours.
\[
\text{Distance Travelled} = 750 \text{ km/h} \times 2.5 \text{ hours} = 1875 \text{ km}
\]

#### Final Answer for Section B:

\[
\begin{array}{|c|c|c|}
\hline
\text{Distance Travelled} & \text{Time Taken} & \text{Average Speed} \\
\hline
140 \text{ km} & 2 \text{ hours} & 70 \text{ km/h} \\
93 \text{ miles} & 3 \text{ hours} & 31 \text{ mph} \\
85 \text{ m} & 20 \text{ seconds} & 4.25 \text{ m/s} \\
6140 \text{ miles} & 8 \text{ hours} & 767.5 \text{ mph} \\
\hline
\end{array}
\]

\[
\begin{array}{|c|c|c|}
\hline
\text{Distance Travelled} & \text{Time Taken} & \text{Average Speed} \\
\hline
50 \text{ km} & 1 \text{ hour} & 50 \text{ km/h} \\
400 \text{ miles} & 4 \text{ hours} & 100 \text{ mph} \\
228 \text{ m} & 30 \text{ seconds} & 7.6 \text{ m/s} \\
1875 \text{ km} & 2 \text{ hours } 30 \text{ minutes} & 750 \text{ km/h} \\
\hline
\end{array}
\]

---

Final Answer:

\[
\boxed{
\begin{array}{|c|c|}
\hline
\text{Time} & \text{Time in hours and minutes} \\
\hline
1.5 \text{ hours} & 1 \text{ hour } 30 \text{ mins} \\
2 \frac{1}{4} \text{ hours} & 2 \text{ hours } 15 \text{ mins} \\
5.75 \text{ hours} & 5 \text{ hours } 45 \text{ mins} \\
3.1 \text{ hours} & 3 \text{ hours } 6 \text{ mins} \\
4 \frac{2}{5} \text{ hours} & 4 \text{ hours } 24 \text{ mins} \\
\hline
\end{array}
}
\]
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Distance Travelled} & \text{Time Taken} & \text{Average Speed} \\
\hline
140 \text{ km} & 2 \text{ hours} & 70 \text{ km/h} \\
93 \text{ miles} & 3 \text{ hours} & 31 \text{ mph} \\
85 \text{ m} & 20 \text{ seconds} & 4.25 \text{ m/s} \\
6140 \text{ miles} & 8 \text{ hours} & 767.5 \text{ mph} \\
\hline
\end{array}
}
\]
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Distance Travelled} & \text{Time Taken} & \text{Average Speed} \\
\hline
50 \text{ km} & 1 \text{ hour} & 50 \text{ km/h} \\
400 \text{ miles} & 4 \text{ hours} & 100 \text{ mph} \\
228 \text{ m} & 30 \text{ seconds} & 7.6 \text{ m/s} \\
1875 \text{ km} & 2 \text{ hours } 30 \text{ minutes} & 750 \text{ km/h} \\
\hline
\end{array}
}
\]