Block 1 - Answers

Answer 1.1

They are currently half way through the journey.

$&= 1000 \unit{m} \times \frac{1}{2} \cdot\cdot &= 500 \unit{m}$

The shortcut's distance is the distance they are now, and the distance of the garden.

$&= 500 \unit{m} + 30 \unit{m} \cdot\cdot &= 530 \unit{m}$

The distance saved, is the difference between the distance of the original journey and the shortcut.

$&= 1000 \unit{m} - 530 \unit{m} \cdot\cdot &= 470 \unit{m}$

The new journey is 530 metres long, and they have saved 470 metres by taking the shortcut.

The first step is to work out how many bricks are used in one layer of the tower.

Bricks used in the width and length of the tower

$w &= \frac{25 \unit{cm}}{5 \unit{cm}} = 5 \unit{blocks} \cdot\cdot l &= \frac{25 \unit{cm}}{1 \unit{cm}} = 25 \unit{blocks}$

So the number of blocks in one layer is;

$&= 5 \unit{blocks} \times 25 \unit{blocks} \cdot\cdot &= 125 \unit{blocks}$

There were 15000 blocks used, so there are 120 layers of blocks.

$&= \frac{15000 \unit{blocks}}{125 \unit{blocks}} \cdot\cdot &= 120 \unit{blocks}$

Each block is 1.5cm high, so the height of the tower is.

$&= 120 \unit{blocks} \times 1.5 \unit{cm} \cdot\cdot &= 180 \unit{cm}$

The tower is 180 cm high.