Question

question 5: laura goes for a cycle from her house to the post office, 4km away.
(a) how long did it take laura to cycle to the post office?
(b) work out lauras speed cycling to the post office.
(c) how long did laura spend at the post office?
(d) work out lauras speed cycling back home.

Explanation:

Step1: Determine time taken to cycle to post - office

From the graph, Laura starts cycling at \(11:05\) and reaches the post - office at \(11:20\).
The time taken \(t_1=11:20 - 11:05 = 15\) minutes.

Step2: Calculate speed cycling to post - office

The formula for speed \(v=\frac{d}{t}\). The distance \(d = 4\) km and \(t=\frac{15}{60}\) hours (since \(1\) hour \( = 60\) minutes).
\(v_1=\frac{4}{\frac{15}{60}}=\frac{4\times60}{15}=16\) km/h.

Step3: Determine time spent at post - office

The distance from home is constant (at \(4\) km) from \(11:20\) to \(11:40\).
The time spent \(t_2=11:40 - 11:20 = 20\) minutes.

Step4: Calculate speed cycling back home

She starts back at \(11:40\) and reaches home at \(12:00\). The time taken \(t_3=12:00 - 11:40 = 20\) minutes \(=\frac{20}{60}\) hours.
Using \(v=\frac{d}{t}\) with \(d = 4\) km, \(v_2=\frac{4}{\frac{20}{60}}=\frac{4\times60}{20}=12\) km/h.

Answer:

(a) \(15\) minutes.
(b) \(16\) km/h.
(c) \(20\) minutes.
(d) \(12\) km/h.