9. Costa is building a new fence in his garden. He uses 25 planks of wood, each of which is $30 \mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks, as shown in the diagram. The total length of Costa's new fence is 6.9 metres. What is the length in centimetres of the overlap between any pair of adjacent planks?
A 2.4
B 2.5
C 3
D 4.8
E 5
SOLUTION
B

Let the length of the overlap be $y \mathrm{~cm}$. From the diagram in the question, it can be seen that the total length of the fence can be calculated as the total length of the 13 pieces in the lower row in the diagram and the total length of the 12 planks in the upper row of the diagram, with each of the 12 having two overlaps removed. Hence $690=13 \times 30+12 \times(30-2 y)$. Therefore $690=390+360-24 y$ and hence $24 y=60$. This has solution $y=2.5$. Therefore the overlap between adjacent planks is $2.5 \mathrm{~cm}$.