Speed, Distance and Time Worksheet 1: Practice calculating distance and average speed with various units and time intervals.

Problem Explanation and Solution

The worksheet involves calculations related to the relationship between Speed, Distance, and Time. The formula connecting these three variables is:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

From this, we can derive:
- \(\text{Distance} = \text{Speed} \times \text{Time}\)
- \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)

We will solve each part of the worksheet step by step.

---

Section 1: Calculate the distance travelled in each journey

#### a. 3 hours at 40 mph
- Given: Speed = 40 mph, Time = 3 hours
- Formula: Distance = Speed × Time
- Calculation:
\[
\text{Distance} = 40 \, \text{mph} \times 3 \, \text{hours} = 120 \, \text{miles}
\]
- Answer: Distance = 120 miles

#### b. 55 km/h for 3.5 hours
- Given: Speed = 55 km/h, Time = 3.5 hours
- Formula: Distance = Speed × Time
- Calculation:
\[
\text{Distance} = 55 \, \text{km/h} \times 3.5 \, \text{hours} = 192.5 \, \text{km}
\]
- Answer: Distance = 192.5 km

#### c. 4 seconds at 3 m/s
- Given: Speed = 3 m/s, Time = 4 seconds
- Formula: Distance = Speed × Time
- Calculation:
\[
\text{Distance} = 3 \, \text{m/s} \times 4 \, \text{seconds} = 12 \, \text{m}
\]
- Answer: Distance = 12 m

#### d. 5.25 hours at 50 km/h
- Given: Speed = 50 km/h, Time = 5.25 hours
- Formula: Distance = Speed × Time
- Calculation:
\[
\text{Distance} = 50 \, \text{km/h} \times 5.25 \, \text{hours} = 262.5 \, \text{km}
\]
- Answer: Distance = 262.5 km

#### e. 30 mph for 20 minutes
- Given: Speed = 30 mph, Time = 20 minutes
- Note: Convert time from minutes to hours. There are 60 minutes in an hour, so:
\[
20 \, \text{minutes} = \frac{20}{60} \, \text{hours} = \frac{1}{3} \, \text{hours}
\]
- Formula: Distance = Speed × Time
- Calculation:
\[
\text{Distance} = 30 \, \text{mph} \times \frac{1}{3} \, \text{hours} = 10 \, \text{miles}
\]
- Answer: Distance = 10 miles

---

Section 2: Calculate the average speed of each journey

#### a. 150 miles in 5 hours
- Given: Distance = 150 miles, Time = 5 hours
- Formula: Speed = Distance ÷ Time
- Calculation:
\[
\text{Speed} = \frac{150 \, \text{miles}}{5 \, \text{hours}} = 30 \, \text{mph}
\]
- Answer: Speed = 30 mph

#### b. 120 km in 3 hours
- Given: Distance = 120 km, Time = 3 hours
- Formula: Speed = Distance ÷ Time
- Calculation:
\[
\text{Speed} = \frac{120 \, \text{km}}{3 \, \text{hours}} = 40 \, \text{km/h}
\]
- Answer: Speed = 40 km/h

#### c. 20 m in 4 seconds
- Given: Distance = 20 m, Time = 4 seconds
- Formula: Speed = Distance ÷ Time
- Calculation:
\[
\text{Speed} = \frac{20 \, \text{m}}{4 \, \text{seconds}} = 5 \, \text{m/s}
\]
- Answer: Speed = 5 m/s

#### d. 87.5 miles in 3.5 hours
- Given: Distance = 87.5 miles, Time = 3.5 hours
- Formula: Speed = Distance ÷ Time
- Calculation:
\[
\text{Speed} = \frac{87.5 \, \text{miles}}{3.5 \, \text{hours}} = 25 \, \text{mph}
\]
- Answer: Speed = 25 mph

#### e. 9 km in 45 minutes
- Given: Distance = 9 km, Time = 45 minutes
- Note: Convert time from minutes to hours. There are 60 minutes in an hour, so:
\[
45 \, \text{minutes} = \frac{45}{60} \, \text{hours} = 0.75 \, \text{hours}
\]
- Formula: Speed = Distance ÷ Time
- Calculation:
\[
\text{Speed} = \frac{9 \, \text{km}}{0.75 \, \text{hours}} = 12 \, \text{km/h}
\]
- Answer: Speed = 12 km/h

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Final Answers

#### Section 1: Distance
a. Distance = 120 miles
b. Distance = 192.5 km
c. Distance = 12 m
d. Distance = 262.5 km
e. Distance = 10 miles

#### Section 2: Speed
a. Speed = 30 mph
b. Speed = 40 km/h
c. Speed = 5 m/s
d. Speed = 25 mph
e. Speed = 12 km/h

---

Boxed Final Answer

\[
\boxed{
\begin{array}{ll}
\text{Section 1:} & \text{Section 2:} \\
\text{a. 120 miles} & \text{a. 30 mph} \\
\text{b. 192.5 km} & \text{b. 40 km/h} \\
\text{c. 12 m} & \text{c. 5 m/s} \\
\text{d. 262.5 km} & \text{d. 25 mph} \\
\text{e. 10 miles} & \text{e. 12 km/h} \\
\end{array}
}
\]