N2011 P1 Q9

A company is drilling for oil. Using machine A, the depth drilled on the first day is 256 metres. On each subsequent day, the depth drilled is 7 metres less than on the previous day. Drilling continues daily up to and including the day when a depth of less than 10 metres is drilled. What depth is drilled on the 10th day, and what is the total depth when drilling is completed?[6]

Using machine B, the depth drilled on the first day is also 256 metres. On each subsequent day, the depth drilled is \(\frac89\) of the depth drilled on the previous day. How many days does it take for the depth drilled to exceed 99% of the theoretical maximum total depth?[4]