Use the formula triangle at the top to solve for distance in Section 1 and average speed in Section 2 of this worksheet.

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

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