Answered

2. Susan and Olive start to walk from their home to school in a straight line. First, they walk steadily for 120 meters in 2 minutes, then they run. Susan runs 1500 meters in 5 minutes. The speed of Olive is twice the speed of Susan. Olive arrives at school within 10 minutes after running.

(i) What is the constant speed of Susan and Olive? (Give your answer in [tex]$m / s$[/tex])

3 marks

Distance traveled = 120 m

Time taken = 2 min = 120 s (because 1 min = 60 s)

Average speed:
[tex]\[
\text{Average speed} = \frac{\text{Distance traveled}}{\text{Time taken}} = \frac{120 \, \text{m}}{120 \, \text{s}} = 1 \, \text{m/s}
\][/tex]

(ii) What is the running speed of Susan? (Give your answer in [tex]$m / s$[/tex])

3 marks

[tex]\[
\begin{aligned}
\text{Distance traveled} & = 1500 \, \text{m} \\
\text{Time taken} & = 5 \, \text{min} = 300 \, \text{s} \\
\text{Average speed} & = \frac{\text{Distance traveled}}{\text{Time taken}} = \frac{1500 \, \text{m}}{300 \, \text{s}} = 5 \, \text{m/s}
\end{aligned}
\][/tex]



Answer :

GinnyAnswer
Let's tackle this problem step-by-step, focusing on each part of the question separately.

### Part (i) - Calculating the Constant Speed of Susan and Olive While Walking

#### Given Information:
- Distance traveled while walking: [tex]\(120 \, \text{meters}\)[/tex]
- Time taken while walking: [tex]\(2 \, \text{minutes}\)[/tex], which needs to be converted to seconds. [tex]\(2 \, \text{minutes} = 2 \times 60 \, \text{seconds} = 120 \, \text{seconds}\)[/tex]

#### Calculating the Walking Speed:
The formula for speed is:

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

Using the given data:

[tex]\[ \text{Walking Speed} = \frac{120 \, \text{meters}}{120 \, \text{seconds}} = 1 \, \text{m/s} \][/tex]

Thus, the constant walking speed of both Susan and Olive is [tex]\(1 \, \text{m/s}\)[/tex].

### Part (ii) - Calculating the Running Speed of Susan

#### Given Information:
- Distance Susan runs: [tex]\(1500 \, \text{meters}\)[/tex]
- Time Susan takes to run: [tex]\(5 \, \text{minutes}\)[/tex], which needs to be converted to seconds. [tex]\(5 \, \text{minutes} = 5 \times 60 \, \text{seconds} = 300 \, \text{seconds}\)[/tex]

#### Calculating Susan's Running Speed:
Using the speed formula again:

[tex]\[ \text{Running Speed of Susan} = \frac{1500 \, \text{meters}}{300 \, \text{seconds}} = 5 \, \text{m/s} \][/tex]

Thus, the running speed of Susan is [tex]\(5 \, \text{m/s}\)[/tex].

### Calculating Olive's Running Speed

According to the problem, Olive's running speed is twice that of Susan's running speed.

[tex]\[ \text{Running Speed of Olive} = 2 \times \text{Running Speed of Susan} = 2 \times 5 \, \text{m/s} = 10 \, \text{m/s} \][/tex]

Thus, the running speed of Olive is [tex]\(10 \, \text{m/s}\)[/tex].

By clearly annotating each step and using the given numbers and units, we arrive at the following conclusions:
- The walking speed of both Susan and Olive is [tex]\(1 \, \text{m/s}\)[/tex].
- The running speed of Susan is [tex]\(5 \, \text{m/s}\)[/tex].
- The running speed of Olive is [tex]\(10 \, \text{m/s}\)[/tex].

Other Questions