Munirah cycled from her home to a park. On her way, she had to cycle past a library.

1. Calculate the distance from home to the library using the given speed and time

$\text{Distance} = \text{Speed} \times \text{Time}$
$\text{Distance} = 15 \times \frac{1}{2} = 7.5\text{ km}$

1. Find the distance from home to the library (from part a)

$\text{Distance}_1 = 15 \times \frac{1}{2} = 7.5\text{ km}$

2. Find the total distance of the journey

The first stage is $1 - \frac{2}{5} = \frac{3}{5}$ of the whole journey.
$\frac{3}{5} \text{ of total distance} = 7.5\text{ km}$
$\text{Total distance} = 7.5 \div \frac{3}{5} = 7.5 \times \frac{5}{3} = 12.5\text{ km}$

3. Find the total time taken in hours

$\text{Time}_1 = \frac{1}{2}\text{ h}$
$\text{Time}_2 = 45\text{ mins} = \frac{45}{60}\text{ h} = \frac{3}{4}\text{ h}$
$\text{Total time} = \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4}\text{ h} = 1.25\text{ h}$

4. Calculate the average speed for the whole journey

$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{12.5}{1.25} = 10\text{ km/h}$